The 2010 Specification for Aluminum Structures is the first unified allowable strength design and load and resistance fa...
LUMINUM A LUMINUM ADESIGN ESIGN D ANUAL M MANUAL
2010
Copyright © 2010, The Aluminum Association, Inc. All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form, or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of The Aluminum Association, Inc.
ISBN: 978-0-9826308-0-8
2010 Aluminum Design Manual Table of Contents PART
TITLE
Foreword
I
Specification for Aluminum Structures
II
Specification for Aluminum Structures Commentary
III
Design Guide
IV
Material Properties
V
Section Properties
VI
Design Aids
VII
Illustrative Examples
Appendix 1
SI Guide
Index
FOREWORD The Aluminum Design Manual includes an aluminum structural design specification and accompanying commentary, a supplemental design guide, material properties, properties of common shapes, design aid tables, and illustrative design examples. This edition of the Aluminum Design Manual is the product of the efforts of the Aluminum Association Engineering and Design Task Force, whose members are listed below. The Aluminum Association Engineering and Design Task Force Steve Sunday, Alcoa Inc., Chair Frank Armao, Lincoln Electric Co. Tanya Dolby, Kawneer Company, Inc. Steve Ducotey, Conservatek Industries, Inc. Randy Kissell, The TGB Partnership George Olive, Larson Engineering, Inc. Gerald Orrison, Temcor Teoman Peköz, Cornell University Frank Shoup, Alcoa Inc. Robert W. Walton, Consultant Ronald D. Ziemian, Bucknell University Michael Skillingberg, The Aluminum Association, Inc. The Aluminum Design Manual is offered as a guideline only and The Aluminum Association, Aluminum Association’s Engineering and Design Task Force and members thereof assume no responsibility or liability whatsoever for any information contained herein and make no representation, warranty expressed or implied, or guarantee whatsoever as to the accuracy of the information or the applicability of such information with respect to the design, engineering or construction of any structure. The use of this Manual by members and non-members of The Aluminum Association is voluntary and the issuance or existence of this Manual does not in any respect prevent or restrict any member or non-member from manufacturing, designing, supplying, constructing, or using products not in conformance with this Manual. Please check www.aluminum.org for postings of 2010 Aluminum Design Manual errata.
Aluminum Design Manual
PART I Specification for Aluminum Structures
Foreword The first edition of the Specification for Aluminum Structures was published in November, 1967, followed by subsequent editions in 1971, 1976, 1982, 1986, 1994, 2000, and 2005. This ninth edition of the Specification combines the previously separate allowable stress and load and resistance factor design specifications. The Specification, developed as a consensus document, has been completely reorganized and includes new or revised provisions concerning • safety and resistance factors • design for stability • adding 6005A-T61 and 6082-T6 • notch sensitivity of 6005-T5 and 6105-T5 • a glossary • shear yield strengths • shear strength of tubes • screw pull-over • screw slot pull-out strength • serviceability • evaluating existing structures • axial compressive strength of complex cross sections • fatigue strength of light pole bases • members subject to torsion • local buckling strength of welded elements • design for fire conditions • design of braces The Aluminum Association gratefully acknowledges the efforts of the Engineering Advisory Committee in developing this edition of the Specification. The Aluminum Association Engineering Advisory Committee Steve Sunday, Alcoa Inc., Chair Frank Armao, Lincoln Electric Co. Tanya Dolby, Kawneer Company, Inc. Steve Ducotey, Conservatek Industries, Inc. Randy Kissell, The TGB Partnership George Olive, Larson Engineering, Inc. Gerald Orrison, Temcor Teoman Peköz, Cornell University Frank Shoup, Alcoa Inc. Robert W. Walton, Consultant Ronald D. Ziemian, Bucknell University Michael Skillingberg, The Aluminum Association, Inc. Robert E. Abendroth, Iowa State University Joseph Bowman, Hapco American Flag Francisco Castano, Geometrica, Inc. Terence Cavanagh, Terrapin Testing, Inc. Karen C. Chou, Minnesota State University, Mankato Cynthia Ebert, Larson Engineering, Inc. Michael Feldberg, Valmont Industries, Inc. Andrew J. Hinkle, Wyle James LaBelle, Computerized Structural Design LeRoy Lutz, Computerized Structural Design Craig C. Menzemer, University of Akron Ken Walerius, Permasteelisa North America January 2010
I-3
Guidelines for the Preparation of Technical Inquiries on the Specification for Aluminum Structures Technical inquiries to obtain an interpretation or request a revision to the Specification for Aluminum Structures should be directed to: Vice President, Technology
[email protected] The Aluminum Association 1525 Wilson Blvd, Suite 600 Arlington, VA 22209 www.aluminum.org Comments on other parts of the Aluminum Design Manual are also welcome. Inquiries should be typewritten and include the inquirer’s name, affiliation, and address. Each inquiry should address a single section of the Specification unless the inquiry involves two or more interrelated sections. The section and edition of the Specification should be identified. Requests for interpretations should be phrased, where possible, to permit a “yes” or “no” answer and include the necessary background information, including figures where appropriate. Requests for revisions should include proposed wording for the revision and technical justification. Inquiries are considered at the first meeting of the Engineering and Design Task Force following receipt of the inquiry.
I-4
January 2010
I Specification for Aluminum Structures TABLE OF CONTENTS Numbers in parentheses after section numbers are corresponding ADM 2005 section numbers. Symbols (3.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Chapter A General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 A.1 Scope (1.1, 2.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 A.2 Referenced Documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 A.3 Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 A.3.1 General Properties (3.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 A.3.1.1 Mechanical Properties (6.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 A.3.1.2 Temperature Limits (6.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 A.3.1.3 Tension Coefficient kt (3.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 A.3.2 Wrought Products (1.2, 7.2.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 A.3.3 Castings (8.1, 8.2, 8.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 A.3.4 Filler Metal for Welding (7.1, 8.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 A.3.5 Bolts and Nuts (1.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 A.3.6 Rivets (1.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 A.3.7 Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Chapter B Design Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.1 Section Properties (2.1, 4.9.1, 7.2.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.2 Loads and Load Combinations (2.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.2.1 Building-Type Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.2.2 Bridge-Type Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.2.3 Other Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.3 Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.3.1 Limit States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.3.2 Required Strength (2.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.3.2.1 Design for Strength Using Load and Resistance Factor Design (LRFD). . . . . . . . . . . 30 B.3.2.2 Design for Strength Using Allowable Strength Design (ASD) . . . . . . . . . . . . . . . . . . 30 B.3.3 Design for Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.3.4 Design for Serviceability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.3.5 Design for Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 B.3.6 Design for Fire Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 B.3.7 Design of Braces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 B.4 Buckling Constants (3.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 B.5 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 B.5.1 Width of Flat Elements and Stiffeners (3.4.8, 3.4.8.1, 3.4.9, 3.4.9.1, 3.4.9.2). . . . . . . . . . . . . . . 32 B.5.2 Radius of Curved Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 B.5.3 Thickness of Elements (4.12). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 B.5.4 Strength of Elements in Uniform Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 B.5.4.1 Flat Elements Supported on One Edge (3.4.8, 3.4.8.1, 3.4.15) . . . . . . . . . . . . . . . . . . 33 B.5.4.2 Flat Elements Supported on Both Edges (3.4.9, 3.4.16). . . . . . . . . . . . . . . . . . . . . . . . 34 B.5.4.3 Flat Elements Supported on One Edge and with a Stiffener on the Other Edge (3.4.9.1, 3.4.16.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 B.5.4.4 Flat Elements Supported on Both Edges and with an Intermediate Stiffener (3.4.9.2, 3.4.16.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 B.5.4.5 Curved Elements Supported on Both Edges (3.4.10, 3.4.16.1) . . . . . . . . . . . . . . . . . . 36 B.5.4.6 Flat Elements Alternate Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
January 2010
I-5
B.5.5 Strength of Elements in Flexure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 B.5.5.1 Flat Elements Supported on Both Edges (3.4.18). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 B.5.5.2 Flat Elements Supported on Tension Edge, Compression Edge Free (3.4.17). . . . . . . 37 B.5.5.3 Flat Elements Supported on Both Edges and with a Longitudinal Stiffener (3.4.19, 4.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 B.5.5.4 Flat Elements Alternate Method (4.13) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 B.5.6 Elastic Buckling Stress of Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 B.6 Fabrication and Erection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 B.7 Evaluation of Existing Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Chapter C Design for Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 C.1 General Stability Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 C.2 Calculation of Required Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 C.3 Calculation of Available Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Chapter D Design of Members for Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 D.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 D.2 Tensile Strength (3.4.1, 7.2.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 D.3 Area Determination. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 D.3.1 Net Area (5.1.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 D.3.2 Effective Net Area (5.1.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Chapter E Design of Members for Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 E.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 E.2 Effective Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 E.3 Member Buckling (3.4.7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 E.3.1 Flexural Buckling (3.4.7.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 E.3.2 Torsional and Flexural-Torsional Buckling (3.4.7.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 E.4 Local Buckling (4.7.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 E.4.1 Weighted Average Local Buckling Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 E.4.2 Alternate Local Buckling Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 E.5 Interaction Between Member Buckling and Local Buckling (4.7.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 E.6 Welded Compression Members. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 E.6.1 Compression Members with Transverse Welds (7.2.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 E.6.2 Compression Members with Longitudinal Welds (7.2.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 Chapter F Design of Members for Flexure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.1.1 Bending Coefficient Cb. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.1.1.1 Doubly Symmetric Shapes (4.9.4.1, 4.9.4.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.1.1.2 Singly Symmetric Shapes (4.9.4.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.2 Open Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.2.1 Lateral-Torsional Buckling (3.4.11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.2.2 Effective Radius of Gyration rye. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.2.2.1 Shapes Symmetric About the Bending Axis (4.9.1). . . . . . . . . . . . . . . . . . . . . . . . . . . 43 F.2.2.2 Singly Symmetric Shapes Unsymmetric about the Bending Axis (4.9.2). . . . . . . . . . 44 F.2.2.3 Shapes Unsymmetric about the Bending Axis (4.9.3). . . . . . . . . . . . . . . . . . . . . . . . . 44 F.2.3 Interaction Between Local Buckling and Lateral-Torsional Buckling (4.7.5). . . . . . . . . . . . . . . 45 F.3 Closed Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 F.3.1 Lateral-Torsional Buckling (3.4.14). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 F.4 Rectangular Bars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 F.4.1 Yielding and Rupture (3.4.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 F.4.2 Lateral-Torsional Buckling (3.4.13). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 F.5 Single Angles (4.11) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 F.5.1 Bending About Geometric Axes (4.11.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 F.5.2 Bending About Principal Axes (4.11.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 F.6 Pipes and Round Tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F.6.1 Yielding and Rupture (3.4.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F.6.2 Local Buckling (3.4.12). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 I-6
January 2010
F.7 F.8
F.9
Rods (3.4.4, 3.4.13). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Elements of Flexural Members. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F.8.1 Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F.8.1.1 Elements in Uniform Tension (3.4.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F.8.1.2 Elements in Flexure (3.4.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F.8.2 Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 F.8.2.1 Elements in Uniform Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 F.8.2.2 Elements in Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 F.8.2.3 Alternate Compressive Flexural Strength (4.13) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 F.8.3 Weighted Average Flexural Strength (4.7.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 Welded Flexural Members. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 F.9.1 Flexural Members with Transverse Welds (7.2.1, 7.2.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 F.9.2 Flexural Members with Longitudinal Welds (7.2.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Chapter G Design of Members for Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 G.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 G.2 Members with Flat Webs Supported on Both Edges (3.4.20, 3.4.21). . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 G.3 Round or Oval Tubes (4.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Chapter H Design of Members for Combined Forces and Torsion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 H.1 Members Subject to Flexure and Axial Force (4.1.1, 4.1.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 H.2 Members Subject to Torsion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 H.2.1 Round or Oval Tubes (4.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 H.2.2 Rectangular Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 H.2.3 Rods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 H.3 Members Subject to Torsion, Flexure, Shear, and/or Axial Compression (4.3, 4.4). . . . . . . . . . . . . . . . . 52 H.3.1 Flat Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 H.3.2 Curved Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Chapter I reserved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter J Design of Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.1.1 Design Basis (5.1.7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.1.2 Fasteners in Combination with Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.1.3 Maximum Spacing of Fasteners (5.1.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.2 Welds (7.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.2.1 Groove Welds (7.3.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.2.1.1 Complete Penetration and Partial Penetration Groove Welds (7.3.1.1). . . . . . . . . . . . 54 J.2.1.2 Effective Area (7.3.1.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.2.1.3 Strength (7.3.1.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 J.2.2 Fillet Welds (7.3.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 J.2.2.1 Effective Throat and Effective Length (7.3.2.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 J.2.2.2 Strength (7.3.2.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 J.2.3 Plug and Slot Welds (7.3.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 J.2.3.1 Effective Area (7.3.3.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 J.2.3.2 Strength (7.3.3.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 J.2.4 Stud Welds (7.3.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 J.2.5 Post-Weld Heat Treating (7.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 J.3 Bolts (5.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 J.3.1 Bolt Material (5.2.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 J.3.2 Holes and Slots for Bolts (5.2.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 J.3.3 Minimum Spacing of Bolts (5.2.6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 J.3.4 Minimum Edge Distance of Bolts (5.1.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 J.3.5 Bolt Tension (5.2.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 J.3.6 Bolt Shear (5.2.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 J.3.7 Bolt Bearing (3.4.5, 5.2.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 January 2010
I-7
J.3.8
J.4
J.5
J.6
J.7 J.8
J.9
Slip-Critical Bolted Connections (5.2.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 J.3.8.1 General (5.2.8.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 J.3.8.2 Material (5.2.8.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 J.3.8.3 Holes (5.2.8.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 J.3.8.4 Design for Strength (5.2.8.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 J.3.8.5 Design for Slip Resistance (5.2.8.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 J.3.8.6 Washers (5.2.8.6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 J.3.9 Lockbolts (5.2.7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 J.3.10 Long Grips (5.1.6) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Rivets (5.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.1 Rivet Material (5.3.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.2 Holes for Cold-Driven Rivets (5.3.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.3 Minimum Spacing of Rivets (5.3.6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.4 Minimum Edge Distance of Rivets (5.1.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.5 Rivet Tension (5.3.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.6 Rivet Shear (5.3.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.7 Rivet Bearing (3.4.5, 5.3.5) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.8 Blind Rivets (5.3.7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.4.9 Hollow-End (Semi-Tubular) Rivets (5.3.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 Tapping Screws (5.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.5.1 Screw Material (5.4.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 J.5.2 Holes for Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 J.5.3 Minimum Spacing of Screws (5.4.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 J.5.4 Minimum Edge Distance of Screws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 J.5.5 Screwed Connection Tension (5.4.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 J.5.5.1 Pull-Out. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 J.5.5.1.1 Screws in Holes (5.4.2.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 J.5.5.1.2 Screws in Screw Slots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 J.5.5.2 Pull-Over (5.4.2.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 J.5.5.3 Screw Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 J.5.6 Screwed Connection Shear (5.4.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 J.5.6.1 Screw Bearing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 J.5.6.2 Screw Tilting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 J.5.6.3 Screw Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Affected Elements of Members and Connectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 J.6.1 Strength of Connectors in Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 J.6.2 Strength of Connectors in Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 J.6.3 Block Shear Strength (5.1.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 J.6.4 Strength of Connectors in Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Bearing Strength of Flat Surfaces and Pins (3.4.6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 Flanges and Webs with Concentrated Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 J.8.1 Crippling of Flat Webs (4.7.7). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 J.8.2 Bearing Stiffeners (4.6.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 J.8.3 Combined Crippling and Bending of Flat Webs (4.7.8). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 Roofing and Siding Connections (5.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 J.9.1 Endlaps (5.5.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 J.9.2 Sidelaps (5.5.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 J.9.3 Fasteners in Laps (5.5.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Chapter K reserved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter L Design for Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 L.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 L.2 Camber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 L.3 Deflections (4.7.6). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 L.4 Vibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 L.5 Wind-Induced Motion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 L.6 Expansion and Contraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 L.7 Connection Slip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 I-8
January 2010
Chapter M Fabrication and Erection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.1 Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.1.1 Punch and Scribe Marks (6.1.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.1.2 Temperature Correction (6.1.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.2 Cutting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.2.1 Methods (6.2.1, 6.2.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.2.2 Edge Quality (6.2.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.2.3 Re-entrant Corners (6.2.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.3 Heating (6.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.4 Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.4.1 Fabrication Methods (6.4.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.4.2 Hole Alignment (6.4.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.5 Bending (6.10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.6 Finishes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.6.1 Where Protective Coating Is Required (6.6.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.6.2 Surface Preparation (6.6.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.6.3 Abrasion Blasting (6.8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.7 Contact with Dissimilar Materials (6.7) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.7.1 Steel (6.7.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.7.2 Wood, Fiberboard, or Other Porous Materials (6.7.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 M.7.3 Concrete or Masonry (6.7.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.7.4 Runoff from Heavy Metals (6.7.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.8 Fabrication Tolerances (6.9) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.9 Welding (7.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.10 Bolt Installation (5.2.8.7, 6.11.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.11 Riveting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.11.1 Driven Head (6.5.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.11.2 Hole Filling (6.5.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.11.3 Defective Rivets (6.5.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 M.12 Erection Tolerances (6.11.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Appendix 1 Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 1.1 General Provisions (9.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 1.2 Test Loading and Deflections (9.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 1.3 Number of Tests and the Evaluation of Test Results (9.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 1.3.1 Tests for Determining Mechanical Properties (9.3.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 1.3.2 Tests for Determining Structural Performance (9.3.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 1.4 Testing Roofing and Siding (9.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1.4.1 Test Method (9.4.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1.4.2 Different Thicknesses (9.4.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1.4.3 Design and Allowable Strengths (9.4.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 1.4.4 Deflections (9.4.4) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Appendix 2 reserved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 3 Design for Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.1 General Provisions (4.8) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.2 Constant Amplitude Loading (4.8.1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3 Variable Amplitude Loading (4.8.2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Appendix 4 Design for Fire Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.1.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.1.2 Performance Objectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.1.3 Load Combinations and Required Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 January 2010
I-9
4.2
4.3
Design for Fire Conditions by Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.1 Design-Basis Fire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 4.2.1.1 Localized Fire. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1.2 Post-Flashover Compartment Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1.3 Exterior Fires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1.4 Fire Duration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1.5 Active Fire Prevention Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.2 Temperatures in Structural Systems under Fire Conditions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.3 Material Properties at Elevated Temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.3.1 Mechanical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.3.2 Thermal Expansion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.3.3 Specific Heat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.4 Structural Design Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.4.1 General Structural Integrity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.4.2 Strength Requirements and Deformation Limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.4.3 Methods of Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.4.3.1 Advanced Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.4.3.2 Simple Methods of Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 4.2.4.4 Design Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 Design by Qualification Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.3.1 Qualification Standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.3.2 Restrained Construction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Appendix 5 Evaluation of Existing Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.2 Material Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.2.1 Wrought and Cast Products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.2.2 Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.2.3 Bolts and Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.3 Evaluation by Structural Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.3.1 Dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.3.2 Strength Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.3.3 Serviceability Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.4 Evaluation by Load Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 5.5 Evaluation Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 Appendix 6 Design of Braces for Columns and Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.1.1 Bracing Types. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.1.2 Bracing Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.2 Column Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.2.1 Relative Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.2.2 Nodal Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.3 Beam Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 6.3.1 Lateral Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3.1.1 Relative Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3.1.2 Nodal Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3.2 Torsional Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3.2.1 Nodal Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 6.3.2.2 Continuous Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 6.4 Beam-Column Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
I-10
January 2010
Symbols The section numbers in which the symbol appears is given in parentheses after the symbol. Ab = nominal cross-sectional area of the bolt (unthreaded body area) (J.3.8.4) Ae = net effective area (D.2, D.3.2) Af = area of the member farther than 2c/3 from the neutral axis, where c is the distance from the neutral axis to the extreme compression fiber (F.9.2) Ag = gross cross-sectional area (B.5.4, D.2, E.3, E.3.2, E.4.1, E.4.2, E.5, E.6.2, F.2.2.3, F.8.1.1, G.1, G.3) Agc = gross cross sectional area of the element in compression (B.5.5) Agt = gross cross sectional area of the element in tension (F.8.1.2, J.6.3) Agv = gross area in shear (J.6.3) Ai = area of element i (E.4.1) AL = cross-sectional area of the longitudinal stiffener (B.5.5.3) An = net area (D.3.1, D.3.2) Ant = net area in tension (J.6.3) Anv = net area in shear (J.6.3) Apb = projected bearing area (J.7) Ar = root area of the screw (J.5.5.3, J.5.6.3) As = area of the intermediate stiffener (B.5.4.4) Asn = thread stripping area of internal thread per unit length of engagement (J.5.5.1.1) Aw = web area (G.2) Awe = effective area of a weld (J.2.1.2, J.2.1.3, J.2.3.1, J.2.3.2) Awz = cross-sectional area of the weld-affected zone, which extends 1 in. (25 mm) to each side of the centerline of a weld (B.5.4, D.2, E.6.2, F.8.1.1, F.9.2, G.1) Awzc = cross sectional area of the weld-affected zone in compression (B.5.5) Awzt = cross sectional area of the weld-affected zone in tension (F.8.1.2) Bbr = buckling constant intercept for bending compression in flat elements (B.4, B.5.5.1, B.5.5.2, B.5.5.3, B.5.5.4, F.4.2, F.5) Bc = buckling constant intercept for compression in columns and beam flanges (B.4, B.5.4.4, E.3, F.2.1, F.3.1) Bp = buckling constant intercept for axial compression in flat elements (B.4, B.5.4.1, B.5.4.2, B.5.4.6, F.5) Bs = buckling constant intercept for shear in flat elements (B.4, G.2, G.3, H.2.1) Bt = buckling constant intercept for axial compression in curved elements (B.4, B.5.4.5, F.6.2) Btb = buckling constant intercept for bending compression in curved elements (B.4, F.6.2) C = torsional shear constant (H.2.2) January 2010
Cb = coefficient that accounts for moment gradient along a beam’s length (F.1.1, F.1.1.1, F.1.1.2, F.2.1, F.2.2.3, F.2.3, F.3.1, F.4.2, F.5(c), F.5.1, F.5.2, 6.3.2.1) Cbr = buckling constant intersection for bending compression in flat elements (B.4, B.5.5.2, F.4.2, F.5) Cc = buckling constant intersection for compression in columns and beam flanges (B.4, B.5.4.4, E.3, F.2.1, F.3.1) Cd = brace coefficient (6.3.1.1, 6.3.1.2) Cf = coefficient used to determine the allowable stress range for fatigue (3.2, 3.3) Cn = correction factor for the number of tests (1.3.2) Cp = buckling constant intersection for axial compression in flat elements (B.4, B.5.4.1, F.5) Cpov = coefficient for determining the pull-over strength of a screw (J.5.5.2) Cs = buckling constant intersection for shear in flat elements (B.4, G.2, G.3, H.2.1) Ct = buckling constant intersection for axial compression in curved elements (B.4, B.5.4.5, F.6.2) Ctb = buckling constant intersection for bending compression in curved elements (B.4) Cw = warping constant (E.3.2, F.2.2.3) Cwa, Cwb, Cw1, Cw2, Cw3 = coefficients used to determine web crippling strength (J.8.1) C1 = coefficient used to determine U (F.2.2.3) C2 = coefficient used to determine U (F.2.2.3) D = nominal diameter of the fastener (J.3.2, J.3.5, J.3.6, J.3.7, J.3.10, J.5, J.5.5.1.1, J.5.5.1.2, J.5.5.2, J.5.6.1, J.5.6.2, J.7) D = diameter of a rod (H.2.3) Dbr = buckling constant slope for bending compression in flat elements (B.4, B.5.5.1, B.5.5.2, B.5.5.3, B.5.5.4, F.4.2, F.5) Dc = buckling constant slope for compression in columns and beam flanges (B.4, B.5.4.4, E.3, F.2.1, F.3.1) Dh = nominal diameter of the hole (J.4.6, J.4.7, J.5.5.2) Dn = nominal dead load (1.3.2, 4.1.3, 5.4) Dp = buckling constant slope for axial compression in flat elements (B.4, B.5.4.1, B.5.4.2, B.5.4.6, F.5) DS = depth of a stiffener (B.5.4.3) Ds = buckling constant slope for shear in flat elements (B.4, G.2, G.3, H.2.1) Dss = screw slot inside diameter (J.5.5.1.2) Dt = buckling constant slope for axial compression in curved elements (B.4, B.5.4.5, F.6.2) Dtb = buckling constant slope for bending compression in curved elements (B.4, F.6.2) Dws = larger of the nominal washer diameter and the screw head diameter, but no greater than 5⁄8 in. (16 mm) (J.5.5.2) I-11
E = compressive modulus of elasticity (A.3.1, A.3.2, A.3.3, B.4, B.5.4.1, B.5.4.2, B.5.4.3, B.5.4.4, B.5.4.5, B.5.4.6, B.5.5.1, B.5.5.2, B.5.5.3, B.5.5.4, B.5.6, E.3, E.3.2, E.5, F.2.1, F.2.2.3, F.2.3, F.3.1, F.4.2, F.5, F.5.1, F.5.2, F.6.2, G.2, G.3, H.2.1, J.8.1, 4.2.3.1, 6.3.2.1, 6.3.2.2) Em = compressive modulus of elasticity at elevated temperatures (4.2.3.1) Fb = stress corresponding to the flexural strength (B.5.5, B.5.5.1, B.5.5.2, B.5.5.3, B.5.5.4, F.2.1, F.2.3, F.3.1, F.4.2, F.6.2, F.8, F.8.1.2, F.8.2, F.8.3, H.3.1, H.3.2) Fbo = stress corresponding to the flexural compression strength for an element if no part of the cross section were weld-affected (B.5.5) Fbw = stress corresponding to the flexural compression strength for an element if the entire cross section were weld-affected (B.5.5) Fc = stress corresponding to the uniform compressive strength (B.5.4, B.5.4.1, B.5.4.2, B.5.4.3, B.5.4.4, B.5.4.5, B.5.4.6, E.3, E.4.2, F.8.3, H.3.1, H.3.2) Fci = local buckling stress of element i computed per Section B.5.4.1 through B.5.4.5 (E.4.1) Fco = stress corresponding to the uniform compression strength for an element if no part of the cross section were weld-affected (B.5.4) Fcw = stress corresponding to the uniform compression strength for an element if the entire cross section were weld-affected (B.5.4) Fcy = compressive yield strength (A.3.2, A.3.3, B.4, B.5.4.1, B.5.4.2, B.5.4.3, B.5.4.4, B.5.4.5, B.5.4.6, B.5.5.1, B.5.5.2, B.5.5.3, B.5.5.4, E.3, E.4.1, F.4.1, F.5, F.6.1, F.7, F.8.3, J.8.1) Fcyw = compressive yield strength of weld-affected zones (A.3.2) Fe = elastic buckling stress (B.5.4.6, B.5.5.4, B.5.6, E.3.2, E.5, F.2.3, L.3) Fex = elastic buckling stress for buckling about the x-axis (E.3.2) Fey = elastic buckling stress for buckling about the y-axis (E.3.2, F.2.2.3) Fez = elastic buckling stress for torsional buckling (E.3.2, F.2.2.3) Fm = mean value of the fabrication factor (1.3.2) Fn = shear strength of an A 325 bolt (J.3.8.4) Fs = shear stress corresponding to the shear strength (G.1, G.2, G.3, H.2.1, H.2.2, H.3.1, H.3.2) Fso = shear stress corresponding to the unwelded shear strength (G.1) FST = stress corresponding to the uniform compressive strength of an element supported on both edges (B.5.4.3) Fsu = shear ultimate strength (A.3.2, A.3.5, A.3.6, J.3.6, J.4.6, J.5.6.3, J.6.2, J.6.3) Fsuw = shear ultimate strength of weld-affected zones (A.3.2, G.1, J.2.1.3) I-12
Fsw = shear stress corresponding to the welded shear strength (G.1, J.2.2.2, J.2.3.2) Fsy = shear yield strength (A.3.1, B.4, G.2, G.3, H.2.1, H.2.3, J.6.2, J.6.3) Ft = tensile stress corresponding to the flexural tensile strength (F.8.1.1, F.8.3) Ftu = tensile ultimate strength (A.3.2, A.3.3, A.3.5, D.2, F.4.1, F.6.1, F.7, F.8.1.1, F.8.1.2, J.3.5, J.3.7, J.4.7, J.5.5.1.2, J.5.5.3, J.5.6.1, J.6.3, J.7) Ftum = tensile ultimate strength at elevated temperatures (4.2.3.1) Ftuw = tensile ultimate strength of weld-affected zones (A.3.2, D.2, F.8.1.1, F.8.1.2, J.2.1.3) Ftu1 = tensile ultimate strength of the part in contact with the screw head or washer (J.5.5.2) Ftu2 = tensile ultimate strength of member not in contact with the screw head (J.5.5.1.1, J.5.6.2) Fty = tensile yield strength (A.3.1, A.3.2, A.3.3, D.2, F.4.1, F.6.1, F.7, F.8.1.1, F.8.1.2, J.6.3, 1.4) Ftym = tensile yield strength at elevated temperatures (4.2.3.1) Ftyw = tensile yield strength of weld-affected zones (A.3.2, D.2, F.8.1.1, F.8.1.2) Fty1 = tensile yield strength of the part in contact with the screw head (J.5.5.2) Fty2 = tensile yield strength of member not in contact with the screw head (J.5.5.1.1) FUT = stress corresponding to the uniform compressive strength of an element supported on one edge only (B.5.4.3) G = shear modulus of elasticity (A.3.1, E.3.2, F.2.2.3) Gf = the grip of a bolt (J.3.10) x 02______ + y02 H = 1 - ____ (E.3.2) r 02 Icy = moment of inertia of the compression flange about the y-axis (F.1.1.2, F.2.2.3) If = moment of inertia of the flange group about the cross section’s neutral axis. The flange group consists of the flat elements in uniform compression or uniform tension and their edge or intermediate stiffeners (F.8.3) IL = moment of inertia of the longitudinal stiffener about the web of the beam (B.5.5.3) Io = moment of inertia of a section comprising the stiffener and one half of the width of the adjacent sub-elements and the transition corners between them taken about the centroidal axis of the section parallel to the stiffened element (B.5.4.4) Is = moment of inertia of the transverse stiffener (G.2) Iw = moment of inertia of the web group about the cross section’s neutral axis. The web group consists of the flat elements in flexure and their intermediate stiffeners. (F.8.3) Iw = moment of inertia about the major principal axis (F.5.2) Ix = moment of inertia about the x-axis (E.3.2, F.2.2.3) January 2010
Iy = moment of inertia about the y-axis (E.3.2, F.1.1.2, F.2.2.1, F.2.2.2, F.2.2.3, F.3.1, 6.3.2.1) Iz = moment of inertia about the minor principal axis (F.5.2) J = torsion constant (E.3.2, F.2.2.1, F.2.2.2, F.2.2.3, F.3.1, H.2.1) K = statistical coefficient based on the number of tests n (1.3.1) Ks = a coefficient used to determine the pull-out strength of a screw (J.5.5.1.1) L = member length (E.2, E.3, E.3.1, E.3.2, E.5, E.6.1, F.2.2.3, F.9.1, 6.1, 6.2.2, 6.3.2.1, 6.3.2.2) Lb = length of a beam between brace points or between a brace point and a cantilever’s free end (F.2.1, F.2.2.1, F.2.2.3, F.2.3, F.3.1, F.4.2, F.5.1, F.5.2, 6.1, 6.2.1, 6.2.2, 6.3.1.1, 6.3.1.2, 6.3.2.1, 6.3.2.2, 6.4) LC = length of the connection in the direction of load, measured from the center of fasteners or the end of welds (D.3.2) Le = length of full thread engagement of a screw in a hole or screw slot not including tapping or drilling point (J.5.5.1.1, J.5.5.1.2) Ln = nominal live load (1.3.2, 4.1.3, 5.4) Ls = length of tube between circumferential stiffeners, or overall length if no circumferential stiffeners are present (H.2.1) Lv = length of tube from maximum to zero shear force (G.3) Lwe = effective length of a weld (J.2.1.2, J.2.2.1, J.2.2.2) Lx = unbraced length for buckling about the x-axis (E.3.2) Ly = unbraced length for buckling about the y-axis (E.3.2) Lz = unbraced length for twisting (E.3.2, F.2.2.3) M = bending moment (J.8.3) MA = absolute value of the moment at the quarter point of the unbraced segment (F.1.1.1) MB = absolute value of the moment at the midpoint of the unbraced segment (F.1.1.1) MC = absolute value of the moment at the three-quarter point of the unbraced segment (F.1.1.1) Mc = design or allowable flexural strength determined in accordance with Chapter F (H.1, J.8.3) Me = elastic lateral-torsional buckling moment (F.2.2.3, F.5, F.5.1, F.5.2) Mi = bending strength of member of intermediate thickness ti (1.4.2) Mm = mean value of the material factor (1.3.2) Mmax = absolute value of the maximum moment in the unbraced segment (F.1.1.1, F.1.1.2) Mn = nominal strength moment (F.1, F.2.1, F.2.3, F.3.1, F.4.1, F.4.2, F.5, F.5.1, F.5.2, F.6.1, F.6.2, F.7, F.8, F.8.3, F.9.2) Mnc = nominal strength moment for compression (F.8.3) Mno = lateral-torsional buckling strength if no part of the cross section were weld-affected (F.9.2) Mnt = nominal strength moment for tension (F.8.3) January 2010
Mnw = lateral-torsional buckling strength if the entire cross section were weld-affected (F.9.2) Mr = required flexural strength using LRFD or ASD load combinations (H.1, 6.3.1.1, 6.3.1.2, 6.3.2.1, 6.3.2.2, 6.4) Mrb = required bracing flexural strength using LRFD or ASD load combinations (6.3.2.1) My = yield moment about the axis of bending (F.5) M1 = bending strength of member of thinnest material (1.4.2) M2 = bending strength of member of thickest material (1.4.2) N = length of the bearing at the concentrated force (J.8.1) N = number of cycles to failure (3.2, 3.3) NS = number of stress ranges in the spectrum (3.3) Ns = number of slip planes (J.3.8.5) P = force (J.8.3) Pc = design or allowable axial tensile strength determined in accordance with Chapter D, compressive strength determined in accordance with Chapter E, or concentrated force determined in accordance with Section J.8.1 (H.1, J.8.3) Pn = nominal strength axial force (D.1, D.2, E.1, E.3, E.4.1, E.4.2, E.5, E.6.2) Pno = nominal member buckling strength if no part of the cross section were weld-affected (E.6.2) Pnw = nominal member buckling strength if the entire cross section were weld-affected (E.6.2) Pr = required axial force using LRFD or ASD load combinations (C.2, H.1, 6.2.1, 6.2.2, 6.4) Prb = required bracing strength (6.2.1, 6.2.2, 6.3.1.1, 6.3.1.2) Py = axial yield strength (C.2) R = outside radius of a tube (H.2.1) R = transition radius of a fatigue detail (3.1) Ra = required strength for ASD (B.3.2.2) Rb = radius of curved elements taken at the midthickness of the element (B.5.2, B.5.4.5, B.5.6, E.6.1, F.6.2, F.9.1, G.3, H.2.1) Ri = inside bend radius at the juncture of the flange and web; for extruded shapes, Ri = 0 (J.8.1) Rn = nominal strength (B.3.2.1, B.3.2.2, J.2.1.3, J.2.2.2, J.2.3.2, J.2.4, J.3.5, J.3.6, J.3.7, J.3.8.4, J.3.8.5, J.4.6, J.4.7, J.5.5, J.5.5.1.1, J.5.5.1.2, J.5.5.2, J.5.5.3, J.5.6, J.5.6.1, J.5.6.2, J.5.6.3, J.6.1, J.6.2, J.6.3, J.6.4, J.7, J.8.1) RS = the ratio of minimum stress to maximum stress for fatigue design (3.1) Ru = required strength for LRFD (B.3.2.1) S = section modulus (F.4.1, F.4.2, F.6.1, F.6.2, F.7) Sc = section modulus on the compression side of the neutral axis (F.2.1, F.2.2.1, F.2.2.2, F.2.2.3, F.2.3, F.3.1, F.5, F.5.1, F.8) Se = 1.28√E/Fcy (B.5.4.3) Sn = nominal snow load (4.1.3) I-13
Sra = applied stress range, the algebraic difference between the minimum and maximum calculated stress (3.2) Srd = allowable stress range (3.2, 3.3) Sre = equivalent stress range (3.3) Sri = ith stress range in the spectrum (3.3) St = section modulus on the tension side of the neutral axis (F.8) Sw = size of a weld (J.2.1.2, J.2.2.1, J.2.2.2) Sx = standard deviation of the test results (1.3.1) S1 = slenderness ratio at the intersection of the equations for yielding and inelastic buckling S2 = slenderness ratio at the intersection of the equations for inelastic buckling and elastic buckling T = temperature (A.3.1.1) T = nominal forces and deformations due to the design-basis fire defined in Section 4.2.1 (4.1.3) Tb = minimum fastener tension (J.3.8.5) Tn = nominal torsional strength (H.2, H.2.1, H.2.2, H.2.3) Tuw = tensile strength of the stud in Table J.2.2 or Table J.2.2M (J.2.4) T1 = temperature (A.3.1.1) T2 = temperature (A.3.1.1) U = coefficient used to determine Me (F.2.2.3) V = shear force on the web at the transverse stiffener (G.2) VF = coefficient of variation of the fabrication factor (1.3.2) VM = coefficient of variation of the material factor (1.3.2) Vn = nominal shear strength (G.1, G.2, G.3) VP = coefficient of variation of the ratio of the observed failure loads divided by the average value of all the observed failure loads (1.3.2) VQ = coefficient of variation of the loads (1.3.2) Xa = strength which 99% of the material is expected to exceed with a confidence of 95% (1.3.1) Xi = result of the ith test (1.3.2) Xm = mean of the test results (1.3.1, 1.3.2) a = fraction of the length of a member (F.2.2.3) a = fatigue detail dimension parallel to the direction of stress (3.1) a1 = shorter dimension of rectangular panel (G.2) a2 = longer dimension of rectangular panel (G.2) b = element width (B.5.1, B.5.3, B.5.4, B.5.4.1, B.5.4.2, B.5.4.3, B.5.4.4, B.5.5, B.5.5.1, B.5.5.2, B.5.5.3, B.5.6, F.5, F.5.1, F.5.2, G.1, G.2, J.1.3, L.3) b = fatigue detail dimension normal to the direction of stress and the surface of the base metal (3.1) be = element’s effective width for determining deflections (L.3) bs = stiffener width (6.3.2.1) c = distance from the neutral axis to the extreme fiber (F.9.2) cc = distance from neutral axis to the element extreme fiber with the greatest compression stress (B.5.5.1) ccf = distance from the centerline of the compression flange to the cross section’s neutral axis (F.8.3) I-14
ccs = distance from the cross section’s neutral axis to the extreme fiber of compression flange stiffeners (F.8.3) ccw = distance from the web group’s extreme compression fiber to the cross section’s neutral axis (F.8.3) co = distance from neutral axis to other extreme fiber of the element (see cc) (B.5.5.1) ctf = distance from the extreme tension fiber to the cross section’s neutral axis (F.8.3) ctw = distance from the web group’s extreme tension fiber to the cross section’s neutral axis (F.8.3) d = full depth of the section (F.2.2.1, F.2.2.2, F.4.2, G.2, J.8.1, J.9.1) de = distance from the center of the fastener to the edge of the part in the direction of force (J.3.7, J.4.7, J.5.6.1, J.7) df = the distance between the flange centroids; for T-shapes df is the distance between the flange centroid and the tip of the stem. (F.2.2.3) ds = stiffener’s flat width (B.5.4.3) d1 = distance from the neutral axis to the compression flange (B.5.5.3) e = base for natural logarithms = 2.71828 . . . (1.3.2) f = compressive stress at the toe of the flange (B.5.5.3) fa = maximum compressive stress in the element from the service load combinations (L.3) fb = compressive stress due to flexure (H.3.1, H.3.2) fc = compressive stress due to axial compression (H.3.1, H.3.2) fs = shear stress due to shear and torsion (H.3.1, H.3.2) g = transverse center-to-center spacing (gage) between fastener gage lines (D.3.1, J.1.3) g0 = distance from the shear center to the point of application of the load; g0 is positive when the load acts away from the shear center and negative when the load acts towards the shear center. If there is no transverse load (pure moment cases) g0 = 0. (F.2.2.3) ho = distance between flange centroids (6.3.1.1, 6.3.1.2, 6.3.2.1, 6.3.2.2) hsc = hole factor for slip-critical bolted connections (J.3.8.5) j = _1_ ∫y 3 dA + ∫yx 2 dA - yo (F.2.2.3) 2Ix A A k = effective length factor for buckling (C.3, E.2, E.3, E.3.1, E.3.2, E.5, J.1.3, 6.1, 6.2.2) kt = tension coefficient (A.3.1.3, D.2, F.4.1, F.6.1, F.7, F.8.1.1, F.8.1.2) kx = effective length factor for flexural buckling about the x-axis (E.3.2) ky = effective length factor for flexural buckling about the y-axis (E.3.2) ky = effective length factor for the compression flange about the y-axis (F.2.2.3) kz = effective length factor for torsional buckling (E.3.2, F.2.2.3)
(
)
January 2010
k1 = coefficient for determining the S2 slenderness limit for elements with postbuckling strength (B.4, B.5.4.1, B.5.4.2, B.5.4.6, B.5.5.1, B.5.5.3, B.5.5.4) k2 = coefficient for determining postbuckling strength (B.4, B.5.4.1, B.5.4.2, B.5.4.6, B.5.5.1, B.5.5.3, B.5.5.4) m = coefficient for elements in flexure and supported on both edges (B.5.5.1) m = coefficient used to determine the allowable stress range for fatigue (3.2, 3.3) n = number of threads/in. (mm) (J.3.5, J.3.6, J.5.5.1.1) n = number of nodal braced points in the span (6.3.2.1, 6.3.2.2) n = number of tests (1.3.1, 1.3.2) q = design pressure load for roofing and siding (1.4) r = radius of gyration (E.2, E.3, E.3.1, E.3.2, E.5) ro = polar radius of gyration of the cross section about the shear center (E.3.2, F.2.2.3) rs = stiffener’s radius of gyration about the stiffened element’s mid-thickness (B.5.4.3) rx = radius of gyration about the x-axis (E.3.2, F.2.2.3) ry = radius of gyration about the y-axis (E.3.2, F.2.1, F.2.2.3) rye = effective radius of gyration about the y-axis for lateral-torsional buckling (F.2.1, F.2.2.1, F.2.2.2, F.2.2.3, F.2.3) rz = radius of gyration about the minor principal axis (F.5.2) s = transverse stiffener spacing. For a stiffener composed of a pair of members, one on each side of the web, the stiffener spacing s is the clear distance between the pairs of stiffeners. For a stiffener composed of a member on only one side of the web, the stiffener spacing s is the distance between fastener lines or other connecting lines. (B.5.5.3, G.2) s = longitudinal center-to-center spacing (pitch) of any two consecutive holes (D.3.1, J.1.3) t = element thickness (B.5.4, B.5.4.1, B.5.4.2, B.5.4.3, B.5.4.4, B.5.4.5, B.5.5, B.5.5.1, B.5.5.2, B.5.5.3, B.5.6, E.6.1, F.4.2, F.5, F.5.1, F.5.2, F.6.2, F.9.1, G.1, G.2, G.3, H.2.1, J.1.3, J.3.7, J.4.7, J.5.6.1, J.7, J.8.1,) t = time (A.3.1.1) tavg = average thickness of a tapered thickness element (B.5.3) ti = thickness of intermediate thickness material (1.4.2) tmax = maximum thickness of a tapered thickness element (B.5.3) tmax = thickness of thickest material tested (1.4.2) tmin = minimum thickness of a tapered thickness element (B.5.3) tmin = thickness of thinnest material tested (1.4.2) ts = beam web stiffener thickness (6.3.2.1) tw = beam web thickness (6.3.2.1, 6.3.2.2)
January 2010
t1 = nominal thickness of the part in contact with the screw head or washer (J.5.5.2, J.5.6.2) t1 = time corresponding to temperature T1 (A.3.1.1) t2 = nominal thickness of the part not in contact with the screw head or washer (J.5.6.2) t2 = time corresponding to temperature T2 (A.3.1.1) x– = eccentricity of the connection in the x-axis direction (D.3.2) xo = the shear center’s x-coordinate (E.3.2, F.2.2.3) y– = eccentricity of the connection in the y-axis direction (D.3.2) yo = the shear center’s y-coordinate (E.3.2, F.2.2.3) zo = coordinate along the z-axis of the shear center with respect to the centroid (F.5.2) a = factor used to determine reduced flexural stiffness (C.2) a = ratio of nominal dead load to nominal live load (1.3.2) a = coefficient of thermal expansion (A.3.1) ai = number of cycles in the spectrum of the ith stress range divided by the total number of cycles (3.3) as = coefficient for a longitudinal stiffener (B.5.5.3) bbr = required bracing stiffness (6.2.1, 6.2.2, 6.3.1.1, 6.3.1.2) bo = target reliability index (1.3.2) bsec = web distortional stiffness (6.3.2.1, 6.3.2.2) bTb = required bracing torsional stiffness (6.3.2.1) bw = section property for unequal leg angles (F.5.2) g = density (A.3.1) (tmax – tmin) δ = _________ = a measure of taper in tapered thicktmin ness elements (B.5.3) k = metric conversion factor (Table B.4.1, Table B.4.2) n = Poisson’s ratio (A.3.1) f = resistance factor (B.3.2.1, D.1, E.1, F.1, G.1, H.2, H.3.1, H.3.2, J.2, J.3.5, J.3.6, J.3.7, J.3.8.4, J.3.8.5, J.4.6, J.4.7, J.5.5, J.5.6, J.6.2, J.6.3, J.7, J.8.1, 1.3.2, 6.1) W = safety factor (B.3.2.2, D.1, E.1, F.1, G.1, H.2, H.3.1, H.3.2, J.2, J.3.5, J.3.6, J.3.7, J.3.8.4, J.3.8.5, J.4.6, J.4.7, J.5.5, J.5.6, J.6.2, J.6.3, J.7, J.8.1, 1.3.2, 6.1) q = angle between a stiffener and the stiffened element (B.5.4.3) q = angle between the plane of web and the plane of the bearing surface (q ≤ 90°) (J.8.1) rST = stiffener ___ effectiveness ratio (B.5.4.3, B.5.6) leq = π ___ E = equivalent slenderness ratio for alternate Fe determination of compressive strength for flexure or axial compression (B.5.4.6, B.5.5.4) ls = slenderness ratio of an element with an intermediate stiffener (B.5.4.4, B.5.6) lt = slenderness ratio for round or oval tubes in shear or torsion (G.3, H.2.1) tb = parameter for reduced flexural stiffness (C.2) µ = mean slip coefficient (J.3.8.5)
√
I-15
Glossary allowable strength: nominal strength divided by the safety factor, Rn/W. allowable stress: allowable strength divided by the appropriate section property, such as section modulus or cross section area. aluminum: aluminum or an aluminum alloy. analysis: the rational determination of the effects of loads on and the strength of structures, members, and connections based on appropriate theory, relevant test data, and sound engineering judgment. applicable building code: the building code under which the structure is designed. ASD (Allowable Strength Design): the method of proportioning structural components such that the allowable strength equals or exceeds the required strength of the component under the action of the ASD load combinations. ASD load combination: the load combination in the applicable building code intended for allowable strength design. available strength: for LRFD, design strength; for ASD, allowable strength. beam: a structural member that has the primary function of resisting bending moments. bearing-type connection: a bolted connection where shear forces are transmitted by the bolt bearing against the connection elements. blind rivet: a rivet that can be installed with access to only one side of the parts being joined. block shear rupture: in a connection, the limit state of tension fracture or yielding along one path and shear yielding or fracture along another path. bolt: a headed and externally threaded mechanical device designed for insertion through holes in assembled parts to mate with a nut and normally intended to be tightened or released by turning that nut. bridge-type structure: a structure not addressed by building codes and designed for highway, pedestrian, or rail traffic. buckling: the limit state of a sudden change in the geometry of a structure or any of its elements under a critical loading condition. building-type structure: a structure of the type addressed by a building code. camber: curvature fabricated into a beam or truss so as to compensate for deflection induced by loads. closed shape: a hollow shape that resists lateral-torsional buckling primarily by torsional resistance rather than warping resistance, that is, for which Cw is much less than 0.038JL b2. See Section F.3. column: a structural member that has the primary function of resisting a compressive axial force. contract documents: documents that define the responsibilities of the parties that design, fabricate, or erect the structure. design load: the applied load determined in accordance with either LRFD load combinations or ASD load combinations, whichever is applicable. I-16
design strength: the resistance factor multiplied by the nominal strength, fRn. design stress: the design strength divided by the appropriate section property, such as section modulus or cross section area. effective length: the length of an otherwise identical column with the same strength when analyzed with pinned end conditions. effective length factor: ratio between the effective length and the unbraced length of the member. effective net area: net area modified to account for the effect of shear lag. elastic analysis: structural analysis based on the assumption that the structure returns to its original geometry on removal of the load. element: a component of a shape’s cross section. Elements are connected to other elements only along their longitudinal edges. Elements addressed by the Specification include flat elements, described by their width b and thickness t, and curved elements, described by their mid-thickness radius Rb and thickness t. An Aluminum Association standard I beam, for example, consists of five flat elements: a web element and two elements in each flange. factored load: the product of a load factor and the nominal load. fastener: bolts, rivets, screws, or other connection devices. fatigue: the limit state of crack initiation and growth resulting from repeated application of loads. filler metal: metal to be added in making a welded joint. fillet weld: weld of generally triangular cross section made between intersecting surfaces of elements. flexural buckling: a buckling mode in which a compression member deflects laterally without twist or change in crosssectional shape. flexural-torsional buckling: a buckling mode in which a compression member bends and twists simultaneously without change in cross-sectional shape. gage: transverse center-to-center spacing of fasteners. gauge: a term previously used in referring to the thickness of a wrought product. Thickness is preferred in dimension description. geometric axis: axis parallel to a web, flange, or angle leg. grip: thickness of material through which a fastener passes. lateral-torsional buckling: the buckling mode of a flexural member involving deflection normal to the plane of bending occurring simultaneously with twist about the shear center of the cross-section. limit state: a condition in which a structure or component becomes unfit for service and is judged either to be no longer useful for its intended function (serviceability limit state) or to have reached its ultimate load-carrying capacity (strength limit state). load effect: forces, stresses, and deformations produced in a structural component by the applied loads. January 2010
load factor: a factor that accounts for deviations of the nominal load from the actual load, for uncertainties in the analysis that transforms the load into a load effect and for the probability that more than one extreme load will occur simultaneously. local buckling: the limit state of buckling of a compression element within a cross section. lockbolt: a two piece fastener consisting of a pin (bolt) and collar. The softer, smooth bore collar is mechanically swaged (reduced or tapered by squeezing) onto the pin and into either zero pitch, annular lock grooves or special thread form grooves in a tension-tension installation method. Hydraulic or pneumatic installation tools provide the tension and swaging action. longitudinal centroidal axis: axis through the centroid of a member along its length LRFD (Load and Resistance Factor Design): a method of proportioning structural components such that the design strength equals or exceeds the required strength of the component under the action of the LRFD load combinations. LRFD load combination: a load combination in the applicable building code intended for strength design (load and resistance factor design). member: an individual, discrete component of a larger structure, such as a beam or column. member buckling: flexural, torsional, or flexural-torsional buckling of the overall member. net area: gross area reduced to account for removed material. nominal dimension: designated or theoretical dimension, as in the tables of section properties. nominal load: magnitude of the load specified by the applicable building code. nominal strength: strength of a structure or component (without the resistance factor or safety factor applied) available to resist load effects, as determined in accordance with this Specification. pitch: longitudinal center-to-center spacing of fasteners; center-to-center spacing of bolt threads along the axis of a bolt. post-buckling strength: the load or force that can be carried by an element, member, or frame after initial elastic buckling has occurred. pull-out: the tensile load required to pull a screw out of a threaded part. pull-over: the tensile load required to pull a part over the head of a screw. resistance factor: a factor that accounts for unavoidable deviations of the actual strength from the nominal strength and for the manner and consequences of failure. rivet: a headed and unthreaded mechanical device used to assemble two or more components by an applied force which deforms the plain rivet end to develop a completed mechanical joint. rod: a solid wrought product that is long in relation to its circular cross section, which is not less than 0.375 in. diameter. January 2010
Figure GL.1 TRANSVERSE CROSS SECTION OF A SCREW CHASE
safety factor: a factor that accounts for deviations of the actual strength from the nominal strength, deviations of the actual load from the nominal load, uncertainties in the analysis that transforms the load into a load effect, and for the manner and consequences of failure. screw: a headed and externally threaded fastener held in place by threading into one of the connected parts. screw chase: a groove parallel to the longitudinal axis of an extrusion, intended to retain a screw whose axis is perpendicular to the longitudinal axis of the extrusion. (See Figure GL.1). screw slot: a semi-hollow in an extrusion intended to retain a screw parallel to the axis of the extrusion. (See Figure GL.2). self-drilling screw: a screw that drills and taps its own hole as it is being driven. service load combination: load combinations under which serviceability limit states are evaluated. slip-critical connection: a bolted connection designed to resist movement by friction on the faying surface of the connection under the clamping forces of the bolts. stiffener: a structural element attached or integral to a member to distribute load, transfer shear, or prevent buckling. structural component: member, connector, connecting element or assemblage.
Figure GL.2 TRANSVERSE CROSS SECTION OF A SCREW SLOT I-17
structure: an object, including but not limited to buildings, walls, fences, towers, bridges, railings, signs, and luminaires, designed to support loads. tapping screw: a screw that threads a preformed hole as it is being driven. thread cutting screw: a tapping screw that is installed into a preformed hole, with internal mating threads formed as a result of cutting out the material being tapped to form the relief area of the threaded shank. thread forming screw: a tapping screw that is installed into a preformed hole, with internal mating threads formed as a result of cold flow of the material being tapped into the relief area of the threaded shank.
I-18
torsional buckling: a buckling mode in which a compression member twists about its shear center axis. unbraced length: the length of a member between brace points or between a brace point and a cantilever’s free end, measured between the longitudinal centroidal axes of the bracing members. For columns, brace points are points at which lateral translation is restrained for flexural buckling or twisting is restrained for torsional buckling. For beams, brace points are points at which the compression flange is restrained against lateral deflection or the cross section is restrained against twisting. weld-affected zone: metal within 1in. (25 mm) of the centerline of a weld.
January 2010
Chapter A General Provisions A.1 Scope The Specification for Aluminum Structures, hereafter referred to as the Specification, applies to the design of aluminum load-carrying structures, members, and connections. This Specification includes the symbols, glossary, Chapters A through M, and Appendices 1 through 6. The provisions of this Specification, or a more rigorous analysis, shall be used for all cases addressed by this Specification. Appropriate analysis shall be used for cases not addressed by this Specification.
A.2 Referenced Documents The following documents are referenced in this Specification: Aluminum Association Aluminum Standards and Data 2009 Aluminum Standards and Data 2009 Metric SI Standards for Aluminum Sand and Permanent Mold Castings (2008) American Association of State Highway and Traffic Officials (AASHTO) Guide Specifications for Design of Pedestrian Bridges (1997) Standard Specifications for Highway Bridges (2002) Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals (2009) American Society of Civil Engineers (ASCE) ASCE/SEI 7-05 Minimum Design Loads for Buildings and Other Structures American Society of Mechanical Engineers (ASME) ASME B18.6.4-1999 Thread Forming and Thread Cutting Tapping Screws and Metallic Drive Screws, Inch Series ASME B46.1-2002 Surface Texture, Surface Roughness, Waviness and Lay American Welding Society (AWS) AWS A.5.10/A5.10M:1999(R2007) Specification for Bare Aluminum and Aluminum-Alloy Welding Electrodes and Rods AWS D1.2/D1.2M:2008 Structural Welding Code— Aluminum ASTM International (ASTM) A 123/A 123M-09 Standard Specification for Zinc (HotDip Galvanized) Coatings on Iron and Steel Products A 153/A 153M-09 Standard Specification for Zinc Coating (Hot-Dip) on Iron and Steel Hardware A 193/A 193M-09 Standard Specification for AlloySteel and Stainless Steel Bolting Materials for High Temperature or High Pressure Service and Other Special Purpose Applications January 2010
A 194/A 194M-09 Standard Specification for Carbon and Alloy Steel Nuts for Bolts for High Pressure or High Temperature Service, or Both A 320/A 320M-08 Standard Specification for AlloySteel and Stainless Steel Bolting Materials for Low-Temperature Service A 325-09a Standard Specification for Structural Bolts, Steel, Heat Treated, 120/105 ksi Minimum Tensile Strength A 325M-09 Standard Specification for Structural Bolts, Steel, Heat Treated 830 MPa Minimum Tensile Strength [Metric] A 563-07a Standard Specification for Carbon and Alloy Steel Nuts A 563M-07 Standard Specification for Carbon and Alloy Steel Nuts [Metric] A 641/A 641M-09a Standard Specification for Zinc-Coated (Galvanized) Carbon Steel Wire B 26/B 26M-09 Standard Specification for Aluminum-Alloy Sand Castings B 108/B 108M-08 Standard Specification for AluminumAlloy Permanent Mold Castings B 209-07 Standard Specification for Aluminum and Aluminum-Alloy Sheet and Plate B 209M-07 Standard Specification for Aluminum and Aluminum-Alloy Sheet and Plate [Metric] B 210-04 Standard Specification for Aluminum and Aluminum-Alloy Drawn Seamless Tubes B 210M-05 Standard Specification for Aluminum and Aluminum-Alloy Drawn Seamless Tubes [Metric] B 211-03 Standard Specification for Aluminum and Aluminum-Alloy Bar, Rod, and Wire B 211M-03 Standard Specification for Aluminum and Aluminum-Alloy Bar, Rod, and Wire [Metric] B 221-08 Standard Specification for Aluminum and Aluminum-Alloy Extruded Bars, Rods, Wire, Profiles, and Tubes B 221M-07 Standard Specification for Aluminum and Aluminum-Alloy Extruded Bars, Rods, Wire, Profiles, and Tubes [Metric] B 241/B 241M-02 Standard Specification for Aluminum and Aluminum-Alloy Seamless Pipe and Seamless Extruded Tube B 247-09 Standard Specification for Aluminum and Aluminum-Alloy Die Forgings, Hand Forgings, and Rolled Ring Forgings B 247M-09 Standard Specification for Aluminum and Aluminum-Alloy Die Forgings, Hand Forgings, and Rolled Ring Forgings [Metric] B 308/B 308M-02 Standard Specification for AluminumAlloy 6061-T6 Standard Structural Profiles B 316/B 316M-02 Standard Specification for Aluminum and Aluminum-Alloy Rivet and Cold-Heading Wire and Rods B 429/B 429M-06 Standard Specification for AluminumAlloy Extruded Structural Pipe and Tube I-19
B 456-03 Standard Specification for Electrodeposited Coatings of Copper Plus Nickel Plus Chromium and Nickel Plus Chromium B 557-06 Standard Test Methods for Tension Testing Wrought and Cast Aluminum- and Magnesium-Alloy Products B 557M-07e1 Standard Test Methods for Tension Testing Wrought and Cast Aluminum- and Magnesium-Alloy Products [Metric] B 632/B 632M-08 Standard Specification for AluminumAlloy Rolled Tread Plate B 695-04 Standard Specification for Coatings of Zinc Mechanically Deposited on Iron and Steel B 928/B 928M-09 Standard Specification for High Magnesium Aluminum-Alloy Sheet and Plate for Marine Service and Similar Environments E 119-09c Standard Test Methods for Fire Tests of Building Construction and Materials E 330-02 Standard Test Method for Structural Performance of Exterior Windows, Doors, Skylights and Curtain Walls by Uniform Static Air Pressure Difference E 1592-05 Standard Test Method for Structural Performance of Sheet Metal Roof and Siding Systems by Uniform Static Air Pressure Difference F 436-09 Standard Specification for Hardened Steel Washers F 436M-09 Standard Specification for Hardened Steel Washers [Metric] F 467-08e1 Standard Specification for Nonferrous Nuts for General Use F 467M-06ae2 Standard Specification for Nonferrous Nuts for General Use [Metric] F 468-06e1 Standard Specification for Nonferrous Bolts, Hex Cap Screws, and Studs for General Use F 468M-06e1 Standard Specification for Nonferrous Bolts, Hex Cap Screws, and Studs for General Use [Metric] F 593-02(2008) Standard Specification for Stainless Steel Bolts, Hex Cap Screws, and Studs F 594-08 Standard Specification for Stainless Steel Nuts F 606-09 Standard Test Methods for Determining the Mechanical Properties of Externally and Internally Threaded Fasteners, Washers, Direct Tension Indicators, and Rivets F 606M-07e1 Standard Test Methods for Determining the Mechanical Properties of Externally and Internally Threaded Fasteners, Washers, and Rivets [Metric] Federal Specification TT-P-645B(1) Primer, Paint, Zinc-Molybdate, Alkyd Type Research Council on Structural Connections (RCSC) Specification for Structural Joints Using ASTM A325 or A490 Bolts, 2004
A.3 Material A.3.1 General Properties The properties listed in Table A.3.1 shall be used unless more precise values are specified. I-20
Table A.3.1 GENERAL PROPERTIES Property
Symbol
Poisson’s ratio Shear modulus of elasticity Coefficient of thermal expansion Density Shear yield strength
Value
n G
0.33 3E/8
a
13 × 10-6/°F = 23 × 10-6/°C
g Fsy
0.10 lb/in3 = 2.7 × 103 kg/m3 0.6 Fty
A.3.1.1 Mechanical Properties Except as noted in Section A.3.1.2, the mechanical properties given in Sections A.3.2 through A.3.6 apply to material held at temperatures of 200°F (93°C) or less for any period of time and for the alloys and tempers listed in Table A.3.2 held at the temperatures listed in Table A.3.2 for cumulative periods of time no greater than the times listed in Table A.3.2. When alloys not addressed in Table A.3.2 are heated above 200°F or alloy-tempers addressed in Table A.3.2 are heated beyond the time-temperature limits of Table A.3.2, mechanical properties shall be reduced to the mechanical properties after heating.
Table A.3.2 TIME-TEMPERATURE LIMITS FOR T5 AND T6 TEMPERS OF 6005, 6061, AND 6063 Temperature °F 450 425 400 375 350 325 300 212
°C
Time
230 220 205 190 175 165 150 100
5 min 15 min 30 min 2 hr 10 hr 100 hr 1,000 hr 100,000 hr
Interpolate time (t) for other temperatures (T) using
log t = log t2 +
log(T2 /T) log (t1/t2) log(T2 /T1)
(A.3-1)
where 1 = next lower temperature in Table A.3.2 than T T T2 = next higher temperature in Table A.3.2 than T t1 = time corresponding to T1 t2 = time corresponding to T2 A.3.1.2 Temperature Limits Alloys 535.0, 5083, 5086, 5154, and 5456 shall not be subjected to temperatures greater than 150°F (66°C), except during fabrication in accordance with Section M.3. January 2010
A.3.3 Castings
A.3.1.3 Tension Coefficient kt The tension coefficient kt shall be as listed in Table A.3.3.
Table A.3.3 TENSION COEFFICIENT kt Unwelded
Weld-Affected Zones
2014-T6, -T651, -T6510, -T6511 Alclad 2014-T6, -T651
1.25
–
6005-T5, 6105-T5
1.25
–
6066-T6, -T6510, -T6511
1.1
–
6070-T6, -T62
1.1
–
all others listed in Table A.3.4 and Table A.3.6
1.0
1.0
Alloy and Temper
A.3.2 Wrought Products This Specification applies to the wrought alloys listed in Tables A.3.4, A.3.8, and A.3.9 and produced to the following ASTM specifications: B 209 Aluminum and Aluminum-Alloy Sheet and Plate B 209M Aluminum and Aluminum-Alloy Sheet and Plate [Metric] B 210 Aluminum and Aluminum-Alloy Drawn Seamless Tubes B 210M Aluminum and Aluminum-Alloy Drawn Seamless Tubes [Metric] B 211 Aluminum and Aluminum-Alloy Bar, Rod, and Wire B 211M Aluminum and Aluminum-Alloy Bar, Rod, and Wire [Metric] B 221 Aluminum and Aluminum-Alloy Extruded Bars, Rods, Wire, Profiles, and Tubes B 221M Aluminum and Aluminum-Alloy Extruded Bars, Rods, Wire, Profiles, and Tubes [Metric] B 241/B 241M Aluminum and Aluminum-Alloy Seamless Pipe and Seamless Extruded Tube B 247 Aluminum and Aluminum-Alloy Die Forgings, Hand Forgings, and Rolled Ring Forgings B 247M Aluminum and Aluminum-Alloy Die Forgings, Hand Forgings, and Rolled Ring Forgings [Metric] B 308/B 308M Aluminum-Alloy 6061-T6 Standard Structural Profiles B 316/B 316M Aluminum and Aluminum-Alloy Rivet and Cold-Heading Wire and Rods B 429/B 429M Aluminum-Alloy Extruded Structural Pipe and Tube B 632/B 632M Aluminum-Alloy Rolled Tread Plate B 928/B 928M High Magnesium Aluminum-Alloy Sheet and Plate for Marine Service and Similar Environments Mechanical properties for unwelded metal shall be as listed in Table A.3.4 or A.3.4M. Mechanical properties for weld-affected zones shall be as listed in Table A.3.5 or A.3.5M. January 2010
This Specification applies to cast products listed in Table A.3.6 and produced to the following ASTM specifications: B 26/B 26M Aluminum-Alloy Sand Castings B 108/B 108M Aluminum-Alloy Permanent Mold Castings Dimensional tolerances shall conform to Standards for Aluminum Sand and Permanent Mold Castings. The purchaser shall require the casting producer to report tensile yield strengths. For sand castings, the purchaser shall require that tensile ultimate and tensile yield strengths of specimens cut from castings shall be at least 75% of the values specified in ASTM B 26. Radiographic inspection in accordance with ASTM B 26 Grade C or B 108 Grade C criteria is required. The number of castings radiographed and the lot acceptance criteria shall be as listed in Table A.3.7. Strengths shall be taken from Table A.3.6 or Table A.3.6M. The compressive yield strength Fcy of castings shall be taken as the tensile yield strength Fty. The modulus of elasticity E of castings shall be taken as 10,000 ksi (70,000 MPa). Welded strengths of castings shall be those established in the AWS D1.2 weld procedure qualification test.
A.3.4 Filler Metal for Welding This Specification applies to filler alloys produced to AWS A.5.10/A5.10M and listed in Tables M.9.1 and M.9.2. Mechanical properties for filler metal shall be as listed in Table J.2.1 or Table J.2.1M.
A.3.5 Bolts and Nuts This Specification applies to aluminum fasteners produced to ASTM specifications F 468 Nonferrous Bolts, Hex Cap Screws, and Studs for General Use F 468M Nonferrous Bolts, Hex Cap Screws, and Studs for General Use [Metric] and aluminum nuts produced to ASTM specifications F 467 Nonferrous Nuts for General Use F 467M Nonferrous Nuts for General Use [Metric] Strengths for aluminum bolts shall be as listed in Table A.3.8 or A.3.8M.
A.3.6 Rivets This Specification applies to rivets of material that meets ASTM B 316/B 316M. Strengths for aluminum rivets shall be as listed in Table A.3.9 or Table A.3.9M.
A.3.7 Screws This Specification applies to aluminum tapping screws that meet ASME B18.6.4. I-21
Table A.3.4 MECHANICAL PROPERTIES FOR WROUGHT ALUMINUM PRODUCTS ALLOY
TEMPER
PRODUCT
THICKNESS in.
Ftu ksi
Fty ksi
Fcy ksi
Fsu ksi
E ksi
1100
-H12 -H14
Sheet, Plate, Drawn Tube, Rod & Bar
All All
14 16
11 14
10 13
9 10
10,100 10,100
2014
-T6 -T651 -T6, T6510, T6511 -T6, T651
Sheet Plate Extrusions Rod & Bar, Drawn Tube
0.040 to 0.249 0.250 to 2.000 All All
66 67 60 65
58 59 53 55
59 58 52 53
40 40 35 38
10,900 10,900 10,900 10,900
Alclad 2014
-T6 -T6 -T651
Sheet Sheet Plate
0.025 to 0.039 0.040 to 0.249 0.250 to 0.499
63 64 64
55 57 57
56 58 56
38 39 39
10,800 10,800 10,800
3003
-H12 -H14 -H16 -H18 -H12 -H14 -H16 -H18
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube Drawn Tube Drawn Tube
0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 All All All All
17 20 24 27 17 20 24 27
12 17 21 24 12 17 21 24
10 14 18 20 11 16 19 21
11 12 14 15 11 12 14 15
10,100 10,100 10,100 10,100 10,100 10,100 10,100 10,100
Alclad 3003
-H12 -H14 -H16 -H18 -H14 -H18
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube
0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 0.025 to 0.259 0.010 to 0.500
16 19 23 26 19 26
11 16 20 23 16 23
9 13 17 19 15 20
10 12 14 15 12 15
10,100 10,100 10,100 10,100 10,100 10,100
3004
-H32 -H34 -H36 -H38 -H34 -H36
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube
0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 0.018 to 0.450 0.018 to 0.450
28 32 35 38 32 35
21 25 28 31 25 28
18 22 25 29 24 27
17 19 20 21 19 20
10,100 10,100 10,100 10,100 10,100 10,100
Alclad 3004
-H32 -H34 -H36 -H38 -H131, H241, H341 -H151, H261, H361
Sheet Sheet Sheet Sheet Sheet Sheet
0.017 to 0.249 0.009 to 0.249 0.006 to 0.162 0.006 to 0.128 0.024 to 0.050 0.024 to 0.050
27 31 34 37 31 34
20 24 27 30 26 30
17 21 24 28 22 28
16 18 19 21 18 19
10,100 10,100 10,100 10,100 10,100 10,100
3005
-H25 -H28
Sheet Sheet
0.013 to 0.050 0.006 to 0.080
26 31
22 27
20 25
15 17
10,100 10,100
3105
-H25
Sheet
0.013 to 0.080
23
19
17
14
10,100
5005
-H12 -H14 -H16 -H32 -H34 -H36
Sheet & Plate Sheet & Plate Sheet Sheet & Plate Sheet & Plate Sheet
0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.017 to 2.000 0.009 to 1.000 0.006 to 0.162
18 21 24 17 20 23
14 17 20 12 15 18
13 15 18 11 14 16
11 12 14 11 12 13
10,100 10,100 10,100 10,100 10,100 10,100
5050
-H32 -H34 -H32 -H34
Sheet Sheet Rod & Bar, Drawn Tube Rod & Bar, Drawn Tube
0.017 to 0.249 0.009 to 0.249 All All
22 25 22 25
16 20 16 20
14 18 15 19
14 15 13 15
10,100 10,100 10,100 10,100
5052
-O -H32 -H34 -H36
Sheet & Plate Sheet & Plate, Rod & Bar, Drawn Tube Sheet
0.006 to 3.000 All All 0.006 to 0.162
25 31 34 37
9.5 23 26 29
9.5 21 24 26
16 19 20 22
10,200 10,200 10,200 10,200
I-22
January 2010
Table A.3.4 MECHANICAL PROPERTIES FOR WROUGHT ALUMINUM PRODUCTS (Continued) ALLOY
TEMPER
PRODUCT
THICKNESS in.
Ftu ksi
Fty ksi
Fcy ksi
Fsu ksi
E ksi
5083
-O -H111 -H111 -O -H116, H32, H321 -H116, H32, H321
Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Plate
up thru 5.000 up thru 0.500 0.501 to 5.000 0.051 to 1.500 0.188 to 1.500 1.501 to 3.000
39 40 40 40 44 41
16 24 24 18 31 29
16 21 21 18 26 24
24 24 23 24 26 24
10,400 10,400 10,400 10,400 10,400 10,400
5086
-O -H111 -O -H112 -H112 -H112 -H112 -H116 -H32 -H34
Extrusions Extrusions Sheet & Plate Plate Plate Plate Plate Sheet & Plate Sheet & Plate, Drawn Tube Sheet & Plate, Drawn Tube
up thru 5.000 up thru 5.000 0.020 to 2.000 0.025 to 0.499 0.500 to 1.000 1.001 to 2.000 2.001 to 3.000 All All All
35 36 35 36 35 35 34 40 40 44
14 21 14 18 16 14 14 28 28 34
14 18 14 17 16 15 15 26 26 32
21 21 21 22 21 21 21 24 24 26
10,400 10,400 10,400 10,400 10,400 10,400 10,400 10,400 10,400 10,400
5154
-H38
Sheet
0.006 to 0.128
45
35
33
24
10,300
5454
-O -H111 -H111 -H112 -O -H32 -H34
Extrusions Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Sheet & Plate
up thru 5.000 up thru 0.500 0.501 to 5.000 up thru 5.000 0.020 to 3.000 0.020 to 2.000 0.020 to 1.000
31 33 33 31 31 36 39
12 19 19 12 12 26 29
12 16 16 13 12 24 27
19 20 19 19 19 21 23
10,400 10,400 10,400 10,400 10,400 10,400 10,400
5456
-O -H116 -H32, H321 -H116 -H32, H321 -H116, H32, H321
Sheet & Plate Sheet & Plate Sheet & Plate Plate Plate Plate
0.051 to 1.500 0.188 to 1.250 0.188 to 0.499 1.251 to 1.500 0.500 to 1.500 1.501 to 3.000
42 46 46 44 44 41
19 33 33 31 31 29
19 27 27 25 25 25
26 27 27 25 25 25
10,400 10,400 10,400 10,400 10,400 10,400
6005 6005A
-T5 -T61
Extrusions Extrusions
up thru 1.000 up thru 1.000
38 38
35 35
35 35
24 24
10,100 10,100
6061
-T6, T651 -T6, T6510, T6511 -T6, T651 -T6 -T6
Sheet & Plate Extrusions Rod & Bar Drawn Tube Pipe
0.010 to 4.000 All up thru 8.000 0.025 to 0.500 All
42 38 42 42 38
35 35 35 35 35
35 35 35 35 35
27 24 25 27 24
10,100 10,100 10,100 10,100 10,100
6063
-T5 -T5 -T52 -T6
Extrusions Extrusions Extrusions Extrusions & Pipe
up thru 0.500 0.501 to 1.000 up thru 1.000 All
22 21 22 30
16 15 16 25
16 15 16 25
13 12 13 19
10,100 10,100 10,100 10,100
6066
-T6, T6510, T6511
Extrusions
All
50
45
45
27
10,100
6070
-T6, T62
Extrusions
up thru 2.999
48
45
45
29
10,100
6082
-T6, T6511
Extrusions
0.200 thru 6.000
45
38
38
25
10,100
6105
-T5
Extrusions
up thru 0.500
38
35
35
24
10,100
6351 6351
-T5 -T6
Extrusions Extrusions
up thru 1.000 up thru 0.750
38 42
35 37
35 37
24 27
10,100 10,100
6463
-T6
Extrusions
up thru 0.500
30
25
25
19
10,100
7005
-T53
Extrusions
up thru 0.750
50
44
43
28
10,500
Note: Rod & Bar is rolled or cold finished.
January 2010
I-23
Table A.3.4M MECHANICAL PROPERTIES FOR WROUGHT ALUMINUM PRODUCTS ALLOY
TEMPER
THICKNESS mm
PRODUCT
Ftu MPa
Fty MPa
Fcy MPa
Fsu MPa
E MPa
1100
-H12 -H14
Sheet, Plate, Drawn Tube, Rod & Bar
All All
95 110
75 95
70 90
62 70
69,600 69,600
2014
-T6 -T651 -T6, T6510, T6511 -T6, T651
Sheet Plate Extrusions Rod & Bar, Drawn Tube
1.00 to 6.30 6.30 to 50.00 All All
455 460 415 450
400 405 365 380
405 400 360 365
275 275 240 260
75,200 75,200 75,200 75,200
Alclad 2014
-T6 -T6 -T651
Sheet Sheet Plate
0.63 to 1.00 1.00 to 6.30 6.30 to 12.50
435 440 440
380 395 395
385 400 385
260 270 270
74,500 74,500 74,500
3003
-H12 -H14 -H16 -H18 -H12 -H14 -H16 -H18
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube Drawn Tube Drawn Tube
0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 0.15 to 3.20 All All All All
120 140 165 185 120 140 165 185
85 115 145 165 85 115 145 165
70 95 125 140 75 110 130 145
75 85 95 105 75 85 95 105
69,600 69,600 69,600 69,600 69,600 69,600 69,600 69,600
Alclad 3003
-H12 -H14 -H16 -H18 -H14 -H18
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube
0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 0.15 to 3.20 0.63 to 6.30 0.25 to 12.50
115 135 160 180 135 180
80 110 140 160 110 160
62 90 115 130 105 140
70 85 95 105 85 105
69,600 69,600 69,600 69,600 69,600 69,600
3004
-H32 -H34 -H36 -H38 -H34 -H36
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube
0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 0.15 to 3.20 0.45 to 11.50 0.45 to 11.50
190 220 240 260 220 240
145 170 190 215 170 190
125 150 170 200 165 185
115 130 140 145 130 140
69,600 69,600 69,600 69,600 69,600 69,600
Alclad 3004
-H32 -H34 -H36 -H38 -H131, H241, H341 -H151, H261, H361
Sheet Sheet Sheet Sheet Sheet Sheet
0.40 to 6.30 0.20 to 6.30 0.15 to 4.00 0.15 to 3.20 0.60 to 1.20 0.60 to 1.20
185 215 235 255 215 235
140 165 185 205 180 205
115 145 165 195 150 195
110 125 130 145 125 130
69,600 69,600 69,600 69,600 69,600 69,600
3005
-H25 -H28
Sheet Sheet
0.32 to 1.20 0.15 to 2.00
180 215
150 185
140 170
105 115
69,600 69,600
3105
-H25
Sheet
0.32 to 2.00
160
130
115
95
69,600
5005
-H12 -H14 -H16 -H32 -H34 -H36
Sheet & Plate Sheet & Plate Sheet Sheet & Plate Sheet & Plate Sheet
0.40 to 50.00 0.20 to 25.00 0.15 to 4.00 0.40 to 50.00 0.20 to 25.00 0.15 to 4.00
125 145 165 120 140 160
95 115 135 85 105 125
90 105 125 75 95 110
75 85 95 75 85 90
69,600 69,600 69,600 69,600 69,600 69,600
5050
-H32 -H34 -H32 -H34
Sheet Sheet Rod & Bar, Drawn Tube Rod & Bar, Drawn Tube
0.40 to 6.30 0.20 to 6.30 All All
150 170 150 170
110 140 110 140
95 125 105 130
95 105 90 105
69,600 69,600 69,600 69,600
5052
-O -H32 -H34 -H36
Sheet & Plate Sheet & Plate, Rod & Bar, Drawn Tube Sheet
0.15 to 80.00 All All 0.15 to 4.00
170 215 235 255
65 160 180 200
65 145 165 180
110 130 140 150
70,300 70,300 70,300 70,300
I-24
January 2010
Table A.3.4M MECHANICAL PROPERTIES FOR WROUGHT ALUMINUM PRODUCTS (Continued) ALLOY
TEMPER
PRODUCT
THICKNESS mm
Ftu MPa
Fty MPa
Fcy MPa
Fsu MPa
E MPa
5083
-O -H111 -H111 -O -H116, H32, H321 -H116, H32, H321
Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Plate
up thru 13.00 up thru 12.70 12.70 to 130.00 1.20 to 6.30 4.00 to 40.00 40.00 to 80.00
270 275 275 275 305 285
110 165 165 125 215 200
110 145 145 125 180 165
165 165 160 170 180 165
71,700 71,700 71,700 71,700 71,700 71,700
5086
-O -H111 -O -H112 -H112 -H112 -H116 -H32 -H34
Extrusions Extrusions Sheet & Plate Sheet & Plate Plate Plate Sheet & Plate Sheet & Plate, Drawn Tube Sheet & Plate, Drawn Tube
up thru 130.00 up thru 130.00 0.50 to 50.00 4.00 to 12.50 12.50 to 40.00 40.00 to 80.00 1.60 to 50.00 All All
240 250 240 250 240 235 275 275 300
95 145 95 125 105 95 195 195 235
95 125 95 115 110 105 180 180 220
145 145 145 150 145 145 165 165 180
71,700 71,700 71,700 71,700 71,700 71,700 71,700 71,700 71,700
5154
-H38
Sheet
0.15 to 3.20
310
240
230
165
71,700
5454
-O -H111 -H111 -H112 -O -H32 -H34
Extrusions Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Sheet & Plate
up thru 130.00 up thru 12.70 12.70 to 130.00 up thru 130.00 0.50 to 80.00 0.50 to 50.00 0.50 to 25.00
215 230 230 215 215 250 270
85 130 130 85 85 180 200
85 110 110 90 85 165 185
130 140 130 130 130 145 160
71,700 71,700 71,700 71,700 71,700 71,700 71,700
5456
-O -H116, H32, H321 -H116, H32, H321 -H116, H32, H321
Sheet & Plate Sheet & Plate Plate Plate
1.20 to 6.30 4.00 to 12.50 12.50 to 40.00 40.00 to 80.00
290 315 305 285
130 230 215 200
130 185 170 170
180 185 170 170
71,700 71,700 71,700 71,700
6005 6005A
-T5 -T61
Extrusions Extrusions
up thru 25.00 up thru 25.00
260 260
240 240
240 240
165 165
69,600 69,600
6061
-T6, T651 -T6, T6510, T6511 -T6, T651 -T6 -T6
Sheet & Plate Extrusions Rod & Bar Drawn Tube Pipe
0.25 to 100.00 All up thru 200 0.63 to 12.50 All
290 260 290 290 260
240 240 240 240 240
240 240 240 240 240
185 165 170 185 165
69,600 69,600 69,600 69,600 69,600
6063
-T5 -T52 -T5 -T6
Extrusions Extrusions Extrusions Extrusions & Pipe
up thru 12.50 up thru 25.00 12.50 to 25.00 All
150 150 145 205
110 110 105 170
110 110 105 170
90 90 85 130
69,600 69,600 69,600 69,600
6066
-T6, T6510, T6511
Extrusions
All
345
310
310
185
69,600
6070
-T6, T62
Extrusions
up thru 80.00
330
310
310
200
69,600
6082
-T6, T6511
Extrusions
5.00 thru 150.00
310
260
260
170
69,600
6105
-T5
Extrusions
up thru 12.50
260
240
240
165
69,600
6351 6351
-T5 -T6
Extrusions Extrusions
up thru 25.00 up thru 20.00
260 290
240 255
240 255
165 185
69,600 69,600
6463
-T6
Extrusions
up thru 12.50
205
170
170
130
69,600
7005
-T53
Extrusions
up thru 20.00
345
305
295
195
72,400
Note: Rod & Bar is rolled or cold finished
January 2010
I-25
Table A.3.5 MECHANICAL PROPERTIES FOR WELD-AFFECTED ZONES IN WROUGHT ALUMINUM PRODUCTS ALLOY
TEMPER
PRODUCT
THICKNESS in.
Ftuw ksi
Ftyw ksi
Fcyw ksi
Fsuw ksi
E ksi
1100 1100
All All
Sheet & Plate, Drawn Tube Rod & Bar
11 11
3.5 3.0
3.5 3.0
8 8
10,100 10,100
3003
All
Sheet & Plate, Drawn Tube
14
5
5
10
10,100
Alclad 3003
All
Sheet & Plate, Drawn Tube
13
4.5
4.5
10
10,100
3004 3004
All All
Sheet & Plate Drawn Tube
22 23
8.5 8.5
8.5 8.5
14 14
10,100 10,100
Alclad 3004
All
Sheet
21
8
8
13
10,100
3005
All
Sheet
17
6.5
6.5
12
10,100
5005
All
Sheet & Plate
15
5
5
9
10,100
5050
All
Sheet & Plate, Drawn Tube, Rod & Bar
18
6
6
12
10,100
5052 5052
All All
Sheet & Plate, Rod & Bar Drawn Tube
25 25
9.5 10
9.5 10
16 16
10,200 10,200
5083 5083 5083
All All All
Extrusions Sheet & Plate Plate
39 40 39
16 18 17
16 18 17
24 24 24
10,400 10,400 10,400
5086
All
Sheet & Plate, Extrusions, Drawn Tube
35
14
14
21
10,400
5154
All
Sheet
30
11
11
19
10,300
5454
All
Sheet & Plate, Extrusions
31
12
12
19
10,400
5456 5456
All All
Sheet & Plate Plate
0.188–1.500 1.501–3.000
42 41
19 18
19 17
26 25
10,400 10,400
6005 6005A
T5 T61
Extrusions Extrusions
up thru 1.000 up thru 1.000
24 24
13 13
13 13
15 15
10,100 10,100
6061 6061
T6, T651, T6510, T65111 T6, T651, T6510, T65112
All All
over 0.375
24 24
15 11
15 11
15 15
10,100 10,100
6063
T5, T52, T6
All
17
8
8
11
10,100
6082
T6, T6511
Extrusions
0.200 to 6.000
28
16
16
15
10,100
6105
T5
Extrusions
up thru 0.500
24
13
13
15
10,100
6351 6351
T5, T6 T5, T62
Extrusions Extrusions
over 0.375
24 24
15 11
15 11
15 15
10,100 10,100
6463
T6
Extrusions
up thru 0.500
17
8
8
11
10,100
7005
T53
Extrusions
up thru 0.750
40
24
24
22
10,500
1
0.188 to 1.500 1.501 to 3.000
Notes 1. When welded with 5183, 5356, or 5556 alloy filler regardless of thickness, and when welded with 4043, 5554, or 5654 alloy filler for thicknesses ≤ 0.375 in.. 2. When welded with 4043, 5554, or 5654 alloy filler.
I-26
January 2010
Table A.3.5M MECHANICAL PROPERTIES FOR WELD-AFFECTED ZONES IN WROUGHT ALUMINUM PRODUCTS ALLOY
TEMPER
PRODUCT
THICKNESS mm
Ftuw MPa
Ftyw MPa
Fcyw MPa
Fsuw MPa
E MPa
1100 1100
All All
Sheet & Plate, Drawn Tube Rod & Bar
75 75
25 20
25 20
55 55
69,600 69,600
3003
All
Sheet & Plate, Drawn Tube
95
35
35
70
69,600
Alclad 3003
All
Sheet & Plate, Drawn Tube
90
30
30
70
69,600
3004 3004
All All
Sheet & Plate Drawn Tube
150 160
60 60
60 60
95 95
69,600 69,600
Alclad 3004
All
Sheet
145
55
55
90
69,600
3005
All
Sheet
115
45
45
85
69,600
5005
All
Sheet & Plate
105
35
35
62
69,600
5050
All
Sheet & Plate, Drawn Tube, Rod & Bar
125
40
40
85
69,600
5052 5052
All All
Sheet & Plate, Rod & Bar Drawn Tube
170 170
65 70
65 70
110 110
70,300 70,300
5083 5083
All All
Extrusions Plate
270 270
110 115
110 115
165 165
71,700 71,700
5086
All
Sheet & Plate, Drawn Tube, Extrusions
240
95
95
145
71,700
5154
All
Sheet
205
75
75
130
71,700
5454
All
Sheet & Plate, Extrusions
215
85
85
130
71,700
5456 5456
All All
Plate Plate
6.30 to 38.00 38.00 to 80.00
285 285
125 125
125 120
170 170
71,700
6005 6005A
T5 T61
Extrusions Extrusions
up thru 25.00 up thru 25.00
165 165
90 90
90 90
105 105
69,600 69,600
6061 6061
T6, T651, T6510, T65111 T6, T651, T6510, T65112
All All
over 9.50
165 165
105 80
105 80
105 105
69,600 69,600
6063
T5, T52, T6
All
115
55
55
75
69,600
6082
T6, T6511
Extrusions
5.00 to 150.00
190
110
110
105
69,600
6105
T5
Extrusions
up thru 12.50
165
90
90
105
69,600
6351 6351
T5, T61 T5, T62
Extrusions Extrusions
over 9.50
165 165
105 80
105 80
105 105
69,600 69,600
6463
T6
Extrusions
up thru 12.50
115
55
55
75
69,600
7005
T53
Extrusions
up thru 20.00
275
165
165
155
72,400
6.30 to 80.00
Notes 1. When welded with 5183, 5356, or 5556 alloy filler regardless of thickness, and when welded with 4043, 5554, or 5654 alloy filler for thicknesses ≤ 9.50 mm. 2. When welded with 4043, 5554, or 5654 alloy filler.
January 2010
I-27
Table A.3.6 STRENGTHS OF ALUMINUM CASTINGS Alloy 356.0 A356.0 354.0
Temper T6 T6 T61
Casting Type sand sand permanent mold
C355.0
T61
permanent mold
356.0 A356.0
T6 T61
permanent mold permanent mold
A357.0
T61
permanent mold
359.0
T61
permanent mold
359.0
T62
permanent mold
535.0
F
permanent mold
Ftu ksi 22.5 25.5 36 47 43 30 40 37 33 28.5 33 28 33.7 46 41 33.7 45 40 35.2 47 40 26.2
Fty ksi 15 18 27.7 36 33 22.5 30 30 22 19.5 26 26 27 36 31 25.5 34 30 28.5 38 30 13.5
Note
(1) (2) (3) (1) (2) (3) (1) (1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3) (1)
See Table A.3.6M
Table A.3.6M STRENGTHS OF ALUMINUM CASTINGS Alloy 356.0 A356.0 354.0
Temper T6 T6 T61
Casting Type sand sand permanent mold
C355.0
T61
permanent mold
356.0 A356.0
T6 T61
permanent mold permanent mold
A357.0
T61
permanent mold
359.0
T61
permanent mold
359.0
T62
permanent mold
535.0
F
permanent mold
Ftu MPa 154 176 248 324 297 207 276 255 228 196 228 193 232 317 283 232 310 276 243 324 276 180
Fty MPa 105 124 191 248 228 155 207 207 152 134 179 179 186 248 214 175 234 207 196 262 207 93
Note
(1) (2) (3) (1) (2) (3) (1) (1) (2) (3) (1) (2) (3) (1) (2) (3) (1) (2) (3) (1)
Notes 1. These strengths apply at any location in the casting if the purchaser does not specify that test specimens be cut from castings. 2. These strengths apply in the locations specified by the purchaser if the purchaser specifies such locations. At other locations, the strengths in (1) apply. 3. These strengths apply anywhere in the casting if the purchaser specifies that these strengths shall be met in specimens cut from the casting without designating a location.
I-28
January 2010
Table A.3.7 RADIOGRAPHIC INSPECTION CRITERIA FOR CASTINGS Lot Size
Number of Castings Required to be Radiographed
Number of Castings Required to Meet Grade C to Pass Lot
2 through 50 51 through 500 over 500
2 8 13
2 7 11
Table A.3.8 STRENGTHS OF ALUMINUM BOLTS Alloy and Temper
Shear Ultimate Strength1 Fsu (ksi)
Tensile Ultimate Strength1 Ftu (ksi)
37 25 41
62 42 68
2024-T4 6061-T6 7075-T73
Table A.3.9 STRENGTHS OF ALUMINUM RIVETS Designation Before Driving 2017-T4 2024-T42 2117-T4 2219-T6 6053-T61 6061-T6 7050-T7 7075-T6 7075-T73 7178-T6
Alloy and Temper
Shear Ultimate Tensile Ultimate Strength1 Fsu (MPa) Strength1 Ftu (MPa)
2024-T4 6061-T6 7075-T73 Note: 1. From ASTM B 316/B 316M
255 170 280
425 290 470
33 37 26 30 20 25 39 42 41 46
Note: 1. From ASTM B 316/B 316M
Table A.3.9M STRENGTHS OF ALUMINUM RIVETS
Note: 1. From ASTM B 316/B 316M and F 468
Table A.3.8M STRENGTHS OF ALUMINUM BOLTS
Shear Ultimate Strength Fsu (ksi) (note 1)
Designation Before Driving
Shear Ultimate Strength Fsu (MPa) (note 1)
2017-T4 2024-T42 2117-T4 2219-T6 6053-T61 6061-T6 7050-T7 7075-T6 7075-T73 7178-T6
225 255 180 205 135 170 270 290 280 315
Note: 1. From ASTM B 316/B 316M
January 2010
I-29
Chapter B Design Requirements B.1 Section Properties Section properties such as cross-sectional area, moment of inertia, section modulus, radius of gyration, and torsion and warping constants shall be determined using nominal dimensions. Section properties used to determine bending deflections shall be determined in accordance with Section L.3. Cross section dimensions shall not vary by more than the tolerances given in Aluminum Standards and Data.
B.2 Loads and Load Combinations B.2.1 Building-Type Structures Building-type structures shall be designed for the nominal loads and load combinations given in the applicable building code or contract documents. In the absence of a building code or contract documents, ASCE 7, Minimum Design Loads for Buildings and Other Structures, shall be used.
B.2.2 Bridge-Type Structures Bridge-type structures shall be designed for the nominal loads and load combinations given in the contract documents. In the absence of contract documents, highway bridges shall be designed for the nominal loads and load combinations given in AASHTO’s Standard Specifications for Highway Bridges, and pedestrian bridges shall be designed for the nominal loads and load combinations given in AASHTO’s Guide Specifications for Design of Pedestrian Bridges.
B.2.3 Other Structures Structural supports for highway signs, luminaires, and traffic signals shall be designed for the loads given in Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals. Other structures shall be designed for the loads given in the contract documents. In the absence of contract documents, other structures shall be designed for the loads given in ASCE 7 where applicable.
B.3 Design Basis Designs shall be made according to the provisions for Load and Resistance Factor Design (LRFD) or Allowable Strength Design (ASD). LRFD is limited to building-type structures.
B.3.1 Limit States No applicable strength or serviceability limit state shall be exceeded by the loads and load combinations given in Section B.2.
B.3.2 Required Strength The required strength of structural members and connections shall be determined by structural analysis using the loads and load combinations stipulated in Section B.2. Computation of forces, moments, and deflections shall be I-30
by elastic analysis in accordance with Chapter C. The effect of eccentricities at connections shall be addressed as required by Section J.1.1. B.3.2.1 Design for Strength Using Load and Resistance Factor Design (LRFD) Design using the provisions for Load and Resistance Factor Design (LRFD) meets the requirements of this Specification when the design strength of each structural component equals or exceeds the required strength determined on the basis of the LRFD load combinations. All provisions of this Specification except Section B.3.2.2 shall apply. Design shall satisfy Equation B.3-1: Ru ≤ fRn
(B.3-1)
where Ru = required strength Rn = nominal strength f = resistance factor fRn = design strength Resistance factors for building-type structures shall be as given in this Specification. B.3.2.2 Design for Strength Using Allowable Strength Design (ASD) Design using the provisions for Allowable Strength Design (ASD) meets the requirements of this Specification when the allowable strength of each structural component equals or exceeds the required strength determined on the basis of the ASD load combinations. All provisions of this Specification except Section B.3.2.1 shall apply. Design shall satisfy Equation B.3-2: Ra ≤ Rn /W
(B.3-2)
where Ra = required strength Rn = nominal strength W = safety factor Rn /W = allowable strength Safety factors for building-type structures and bridgetype structures shall be as given in this Specification.
B.3.3 Design for Stability Stability of the structure and its components shall be determined in accordance with Chapter C.
B.3.4 Design for Serviceability Structures and their components shall meet the serviceability requirements given in Chapter L. January 2010
B.3.5 Design for Fatigue
B.3.7 Design of Braces
Structures and their components subjected to repeated loading shall meet the requirements of Appendix 3. Fatigue need not be considered for seismic loads.
Braces for columns and beams shall meet the requirements of Appendix 6.
B.3.6 Design for Fire Conditions Design for fire conditions shall meet the requirements of Appendix 4.
B.4 Buckling Constants Buckling constants B, D, and C shall be determined from Tables B.4.1 and B.4.2. Postbuckling constants k1 and k2 shall be determined from Table B.4.3.
Table B.4.1 BUCKLING CONSTANTS FOR TEMPER DESIGNATIONS BEGINNING WITH O, H, T1, T2, T3, OR T4, AND WELD-AFFECTED ZONES OF ALL TEMPERS
Type of Stress and Member
Intercept
( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( ))
Compression in Columns and Beam Flanges
Fcy Bc = Fcy 1 + ____ 1000κ
Axial Compression in Flat Elements
F__ cy Bp = Fcy 1 + ___ 440κ
Axial Compression in Curved Elements
Fcy Bt = Fcy 1 + ___ __ 6500κ
Bending Compression in Flat Elements
F__ cy Bbr = 1.3Fcy 1 + ___ 340κ
Bending Compression in Curved Elements
Fcy Btb = 1.5Fcy 1 + ____ __ 6500κ
Shear in Flat Elements
sy Bs = Fsy 1 + _F ___ 240κ
1/2
1/3
1/5
1/3
1/5
1/3
Slope
Intersection
( ) __ ___ ( ) ___ __ () ___ ___ ( ) ___ ___ ( ) __ ___ ( )
Bc 6B D = __ ___c c 20 E
1/2
2Bc C = ___ c 3Dc
D = Bp 6Bp p 20 E
1/2
2Bp = ___ C p 3Dp
D = Bt Bt t 3.7 E
1/3
D = Bbr 6Bbr br 20 E D = Btb Btb tb 2.7 E D = Bs 6Bs s 20 E
1/2
1/3
1/2
Ct see note 2 2Bbr C = ___ br 3Dbr
(
Btb - Bt = _____ C tb Dtb - Dt
)
2
2Bs C = ___ s 3Ds
Notes 1. k = 1.0 ksi (6.895 MPa) 2. Ct shall be determined using a plot of curves of limit state stress based on elastic and inelastic buckling or by trial and error solution.
Table B.4.2 BUCKLING CONSTANTS FOR TEMPER DESIGNATIONS BEGINNING WITH T5, T6, T7, T8, OR T9
Type of Stress and Member
Intercept
( ( )) ( ( )) ( ( )) ( ( )) ( ( )) ( ( ))
Slope
Intersection
() __ __ () ___ __ () ___ ___ ( ) ___ ___ ( ) __ __ ()
Compression in Columns and Beam Flanges
F__ cy Bc = Fcy 1 + ___ 2250κ
1/2
Bc B D = __ __c c 10 E
1/2
Bc C = 0.41 __ c Dc
Axial Compression in Flat Elements
F__ cy Bp = Fcy 1 + ____ 1500κ
1/3
D = Bp Bp p 10 E
1/2
Bp C = 0.41 __ p Dp
Axial Compression in Curved Elements
F__ cy__ Bt = Fcy 1 + ___ 50,000κ
D = Bt Bt t 4.5 E
1/3
Bending Compression in Flat Elements
F__ cy Bbr = 1.3Fcy 1 + ___ 340κ
Bending Compression in Curved Elements
Btb = 1.5Fcy 1 + ___F___cy__ 50,000κ
Shear in Flat Elements
sy Bs = Fsy 1 + _F ___ 800κ
1/3
1/5
1/3
1/5
D = Bbr 6Bbr br 20 E D = Btb Btb tb 2.7 E D = Bs Bs s 10 E
1/2
1/2
1/3
Ct see note 2 2Bbr C = ___ br 3Dbr
(
Btb - Bt = _____ C tb Dtb - Dt
)
2
= 0.41 B __s C s Ds
Notes 1. k = 1.0 ksi (6.895 MPa) 2. Ct shall be determined using a plot of curves of limit state stress based on elastic and inelastic buckling or by trial and error solution.
January 2010
I-31
Table B.4.3 POSTBUCKLING CONSTANTS Type of Element Flat Elements in Compression for Temper Designations Beginning with O, H, T1, T2, T3, or T4, and weld-affected zones of all tempers Flat Elements in Compression for Temper Designations Beginning with T5, T6, T7, T8, or T9 Flat Elements in Flexure
k1
k2
0.50
2.04
0.35
2.27
0.50
2.04
B.5 Elements B.5.1 Width of Flat Elements and Stiffeners For flat elements:
of the fillet or bend at the element’s supported edge (Figure B.5.1) b) supported on both edges and flat elements supported on one edge and with a stiffener on the other edge, the element width b is the distance between the toes of the fillets or bends at the element’s supported or stiffened edges (Figures B.5.2 and B.5.3). c) supported on both edges and with an intermediate stiffener, the element width b is the largest distance between the toe of the fillet or bend at the element’s supported edge and the toe of the fillet or bend at the intermediate stiffener (Figure B.5.4). For all flat elements, if the inside corner radius exceeds 4 times the element thickness, the inside radius shall be assumed equal to 4 times the thickness in calculating b. Dimensions and properties of stiffeners shall be determined in accordance with Figures B.5.3 and B.5.4.
B.5.2 Radius of Curved Elements
a) supported on one edge, the element width b is the distance from the element’s unsupported edge to the toe
The radius of curved elements Rb shall be taken at the mid-thickness of the element.
If r > 4t, use r = 4t to calculate b.
Figure B.5.1 FLAT ELEMENTS SUPPORTED ON ONE EDGE
I-32
January 2010
B.5.4 Strength of Elements in Uniform Compression For elements in uniform compression, the stress corresponding to the uniform compression strength is For unwelded members: Fc = Fco
(B.5-3)
For welded members: Fc = Fco(1 - Awz /Ag) + Fcw Awz /Ag
(B.5-4)
where
If r > 4t, use r = 4t to calculate b.
Figure B.5.2 FLAT ELEMENTS SUPPORTED ON BOTH EDGES B.5.3 Thickness of Elements For uniform compression on elements with linearly varying thickness with d ≤ 2.0: a) For tapered thickness elements with the thick edge supported and the thin edge free, the slenderness ratio is (1 - 0.12d)(b/tavg). b) For tapered thickness elements with the thin edge supported and the thick edge free, the slenderness ratio is (b/tavg) c) For tapered thickness elements supported on both edges, the slenderness ratio is (b/tavg).
Fco = stress corresponding to the uniform compression strength calculated using Sections B.5.4.1 through B.5.4.5 for an element if no part of the cross section were weld-affected. Use buckling constants for unwelded metal (Table B.4.1 or Table B.4.2) and strengths from Table A.3.4 or Table A.3.4M. Fcw = stress corresponding to the uniform compression strength calculated using Sections B.5.4.1 through B.5.4.5 for an element if the entire cross section were weld-affected. Use buckling constants for weld-affected zones (Table B.4.1) and strengths from Table A.3.5 or Table A.3.5M. For transversely welded elements with b/t ≤ S1, Fc = Fco. Awz = cross sectional area of the weld-affected zone Ag = gross cross sectional area of the element.
B.5.4.1 Flat Elements Supported On One Edge The stress Fc corresponding to the uniform compression strength of flat elements supported on one edge is:
Limit State
Fc
b/t
yielding
Fcy
b/t ≤ S1
where b = element width tmax + tmin tavg = 2
(B.5-1)
p2E b/t ≥ S2 (5.0b/t)2 in all other columns and all beams: elastic buckling
(tmax - tmin) d = tmin
post-buckling
January 2010
Bp - Fcy S1 = 5.0Dp
inelastic Bp - 5.0Dp b/t S1 < b/t < S2 buckling in columns whose buckling axis is not an axis of symmetry:
= average thickness of the element tmin = minimum thickness of the tapered thickness element tmax = maximum thickness of the tapered thickness element (B.5-2)
Slenderness Limits
k2 √BpE 5.0b/t
b/t ≥ S2
S2 =
S2 =
Cp 5.0
k1 Bp 5.0Dp I-33
If r > 4t, use r = 4t to calculate b.
Figure B.5.3 EDGE STIFFENED ELEMENTS
B.5.4.2 Flat Elements Supported on Both Edges The stress Fc corresponding to the uniform compression strength of flat elements supported on both edges is:
Limit State
Fc
b/t
yielding
Fcy
b/t ≤ S1
inelastic buckling post-buckling
I-34
Slenderness Limits Bp - Fcy S1 = 1.6Dp
Bp -1.6Dp b/t S1 < b/t < S2 k2 √BpE 1.6b/t
b/t ≥ S2
S2 =
k1 Bp 1.6Dp
B.5.4.3 Flat Elements Supported on One Edge and with a Stiffener on the Other Edge For flat elements a) supported on one edge and with a stiffener on the other edge, b) with a stiffener of depth DS ≤ 0.8b, where DS is defined in Figure B.5.3, and c) with a thickness no greater than the stiffener’s thickness, the stress corresponding to the uniform compression strength is Fc = FUT + (FST - FUT)rST
(B.5-5)
January 2010
Line o-o is the neutral axis of the stiffener and element of width b/2 on each side of the stiffener. Io is the moment of inertia of the portion shown in the partial section.
If r > 4t, use r = 4t to calculate b.
Figure B.5.4 FLAT ELEMENTS WITH AN INTERMEDIATE STIFFENER
where FUT is determined using Section B.5.4.1 and neglecting the stiffener FST is determined using Section B.5.4.2 rST = stiffener effectiveness ratio determined as follows: a) rST = 1.0
for b/t ≤ Se /3 (B.5-6)
rs = the stiffener’s radius of gyration about the stiffened element’s mid-thickness. For straight stiffeners of constant thickness (see Figure B.5.3) – rs = ds (sin q)/√3 where ds = the stiffener’s flat width and q = the angle between the stiffener and the stiffened element. Se = 1.28√E/Fcy
(B.5-9)
rs b) rST = _________ ≤ 1.0 b/t 1 9t ___ – __
for Se /3 < b/t ≤ Se (B.5-7) Se 3
Fc for the stiffened element determined using Section B.5.4.3 shall not exceed Fc for the stiffener determined using Section B.5.4.1. For flat elements
rs c) rST = ___________ ≤ 1.0 for Se < b/t < 2Se b/ ___ 1.5t t + 3 (B.5-8) S
a) supported on one edge and with a stiffener on the other edge, and
(
)
(
January 2010
e
)
I-35
b) with a stiffener of depth DS > 0.8b, where DS is defined in Figure B.5.3, or with a thickness greater than the stiffener’s thickness, the stress corresponding to the uniform compression strength is Fc = FUT. B.5.4.4 Flat Elements Supported on Both Edges and with an Intermediate Stiffener The stress Fc corresponding to the uniform compression strength of flat elements supported on both edges and with an intermediate stiffener is:
Limit State
Fc
ls
yielding
Fcy
ls ≤ S1
Bc - Dc ls
S1 < ls < S2
p2 E l2s
ls ≥ S2
inelastic buckling elastic buckling where
()
Slenderness Limits S1 =
Bc - Fcy Dc
S2 = Cc
(B.5-10)
√
Fc shall not exceed Fc determined using Section B.5.4.2 for the sub-elements of the stiffened element. Fc need not be less than Fc determined using Section B.5.4.2 and neglecting the stiffener. B.5.4.5 Curved Elements Supported on Both Edges The stress Fc corresponding to the uniform compression strength of curved elements supported on both edges is: Limit State
Fc
Rb/t
yielding
Fcy
Rb /t ≤ S1
√Rt
b
Slenderness Limits S1 =
(
Bt - Fcy Dt
)
2
S1 < Rb /t < S2
p2 E elastic R √R /t 2 buckling 16 ___b 1+ b t 35
( )(
)
Rb /t ≥ S2
S2 = Ct
For tubes with circumferential welds, use of Section B.5.4.5 is limited by Sections E.6.1 and F.9.1. I-36
Fc
leq
Slenderness Limits
yielding
Fcy
leq ≤ S1
Bp - Fcy S1 = Dp
inelastic buckling Bp - Dpleq S1 < leq < S2 post-buckling k2 √BpE leq ≥ S2 k1Bp S2 = leq Dp ___
√
leq = π ___ E Fe
(B.5-11)
For elements in flexure, the stress corresponding to the flexural compression strength is For unwelded members:
s = area of the stiffener A Io = moment of inertia of a section comprising the stiffener and one half of the width of the adjacent subelements and the transition corners between them taken about the centroidal axis of the section parallel to the stiffened element (Figure B.5.4).
Bt - Dt
Limit State
B.5.5 Strength of Elements in Flexure
1 +__________ As /(bt) b ______________ λs = 4.62 __ t 10.67Io 1 + 1 + ______ 3 bt
inelastic buckling
As an alternate to Sections B.5.4.1 through B.5.4.4, the stress Fc corresponding to the uniform compression strength of flat elements without welds may be determined as:
Fe = the elastic local buckling stress of the cross section determined by analysis
_______________
√
B.5.4.6 Flat Elements Alternate Method
Fb = Fbo
(B.5-12)
For welded members: Fb = Fbo (1 - Awzc /Agc) + Fbw Awzc /Agc
(B.5-13)
where Fbo = stress corresponding to the flexural compression strength calculated using Sections B.5.5.1 through B.5.5.3 for an element if no part of the cross section were weld-affected. Use buckling constants for unwelded metal (Table B.4.1 or Table B.4.2) and mechanical properties from Table A.3.4 or Table A.3.4M. Fbw = stress corresponding to the flexural compression strength calculated using Sections B.5.5.1 through B.5.5.3 for an element if the entire cross section were weld-affected. Use buckling constants for weld-affected zones (Table B.4.1) and mechanical properties from Table A.3.5 or Table A.3.5M. For transversely welded elements with b/t ≤ S1, Fb = Fbo. Awzc = cross sectional area of the weld-affected zone in compression Agc = gross cross sectional area of the element in compression. B.5.5.1 Flat Elements Supported on Both Edges The stress Fb corresponding to the flexural compression strength of flat elements supported on both edges and flat January 2010
elements supported on the compression edge with the tension edge free is: Limit State yielding inelastic buckling postbuckling
Fb
b/t
1.3Fcy
b/t ≤ S1
Slenderness Limits S1 =
Bbr - 1.3Fcy mDbr
Bbr - mDbr b/t S1 < b/t < S2 k2 √BbrE (mb/t)
b/t ≥ S2
S2 =
k1Bbr mDbr
= 1.15 + co /(2cc) m for -1 < co /cc < 1 m = 1.3/(1 - co /cc) for co /cc ≤ -1 m = 0.65 for cc = - co cc = distance from neutral axis to the element extreme fiber with the greatest compression stress co = distance from neutral axis to other extreme fiber of the element Distances to compressive fibers are negative and distances to tensile fibers are positive. B.5.5.2 Flat Elements Supported on Tension Edge, Compression Edge Free The stress Fb corresponding to the flexural compression strength of flat elements supported on the tension edge with the compression edge free is: Limit State yielding inelastic buckling elastic buckling
Fb
b/t
1.3Fcy
b/t ≤ S1
Slenderness Limits S1 =
Bbr - 1.3Fcy 3.5Dbr
Bbr - 3.5Dbr b/t S1 < b/t < S2 πE (3.5b/t)2 2
b/t ≥ S2
S2 =
Cbr 3.5
B.5.5.3 Flat Elements Supported on Both Edges and with a Longitudinal Stiffener The stress Fb corresponding to the flexural compression strength of elements supported on both edges and with a longitudinal stiffener located 0.4d1 from the supported edge that is in compression is: Limit State yielding inelastic buckling postbuckling
Fb
b/t
1.3Fcy
b/t ≤ S1
Slenderness Limits Bbr - 1.3Fcy S1 = 0.29Dbr
Bbr - 0.29Dbr b/t S1 < b/t < S2 k2 √BbrE (0.29b/t)
January 2010
b/t ≥ S2
S2 =
k1Bbr 0.29Dbr
Figure B.5.5 FLAT ELEMENT WITH A LONGITUDINAL STIFFENER The moment of inertia of the longitudinal stiffener IL about the web of the beam shall equal or exceed
[(
)( ) ]
0.02as ftb3 6AL s 2 I = ________ 1 + ___ __ + 0.4 L E bt b
(B.5-14)
where (see Figure B.5.5) L = cross-sectional area of the longitudinal stiffener A d1 = distance from the neutral axis to the compression flange f = compressive stress at the toe of the flange b = clear height of the web s = distance between transverse stiffeners t = web thickness as = 1 for a stiffener consisting of equal members on both sides of the web = 3.5 for a stiffener consisting of a member on only one side of the web For a stiffener consisting of equal members on both sides of the web, the moment of inertia IL shall be the sum of the moments of inertia about the centerline of the web. For a stiffener consisting of a member on one side of the web only, the moment of inertia IL shall be taken about the face of the web in contact with the stiffener. B.5.5.4 Flat Elements Alternate Method As an alternate to Sections B.5.5.1 through B.5.5.3 for flat elements in flexure without welds, the stress Fb corresponding to the flexural strength may be determined as:
Fb
leq
yielding
1.3Fcy
leq ≤ S1
inelastic buckling
Bbr - Dbrleq
S1 < leq < S2
postbuckling
k2 √BbrE leq
leq ≥ S2
Limit State
Slenderness Limits S1 =
Bbr - 1.3Fcy Dbr
S2 =
k1Bbr Dbr I-37
___
√
leq = π ___ E Fe
(B.5-15)
Fe = the elastic local buckling stress of the cross section determined by analysis
B.6 Fabrication and Erection Fabrication and erection shall meet the requirements in Chapter M.
B.5.6 Elastic Buckling Stress of Elements
B.7 Evaluation of Existing Structures
The elastic buckling stress of elements shall be determined using Table B.5.1.
Evaluation of existing structures shall meet the requirements in Appendix 5.
Table B.5.1 ELASTIC BUCKLING STRESS Fe OF ELEMENTS Element Type
Element Stress
Element Support
Fe
flat
uniform compression
supported on both edges
p2E _______ (1.6b/t)2
flat
uniform compression
supported on one edge
2E p _______ (5.0b/t)2
flat
uniform compression
supported on one edge and with a stiffener on the other edge
flat
uniform compression
supported on both edges and with an intermediate stiffener
2E p ___ l 2s
supported on both edges
p2E ___ _________________ Rb √Rb/t 2 16 __ 1 + _____ t 35
curved
uniform compression
p2E p2E (1 - rST) _______ + rST _______
( )(
(5.0b/t)2
(1.6b/t)2
)
Note: ls is determined from equation B.5-10
I-38
January 2010
Chapter C Design for Stability This chapter addresses requirements for the analysis and design of structures for stability.
C.1 General Stability Requirements Stability shall be provided for the structure as a whole and for each of its components. The available strengths of members and connections determined in accordance with Section C.3 shall equal or exceed the required strengths determined in accordance with Section C.2
C.2 Calculation of Required Strengths The required strengths of members and connections of the structure shall be determined from an elastic analysis that considers the effects of each of the following: 1) Flexural, shear, and axial deformations, including all member and connection deformations that contribute to displacements of the structure; 2) Second-order effects including P-D effects (the effect of loads acting on the displaced location of joints or nodes in a structure) and P-d effects (the effect of loads acting on the deflected shape of a member between joints or nodes); 3) Geometric imperfections. The effect of geometric imperfections on the stability of the structure shall be accounted for by analyzing the structure with the members’ points of intersection displaced from their nominal locations by the tolerances specified in the contract documents. The displacements shall be placed to cause the greatest destabilizing effect. 4) Member stiffness reduction due to inelasticity. The effect of member stiffness reduction due to inelasticity on the
January 2010
stability of the structure shall be accounted for by using a reduced stiffness as follows: A factor tb shall be applied to the flexural stiffnesses of all members whose flexural stiffnesses contribute to the stability of the structure, where tb = 1.0 for a Pr /Py ≤ 0.5 tb = 4(a Pr /Py) (1 - a Pr /Py) for a Pr /Py > 0.5 Pr = required axial compressive strength using LRFD or ASD load combinations Py = axial yield strength a = 1.0 (LRFD); a = 1.6 (ASD) 5) Uncertainty in stiffness and strength shall be addressed by applying a factor of 0.8 to all axial, shear, and flexural stiffnesses in the structure. The analysis shall include all gravity loads, including loads on elements that are not part of the lateral load-resisting system. Analysis shall be conducted for either: a) The LRFD load combinations with the results used directly to obtain the required strengths, or b) 1.6 times the ASD load combinations with the results divided by 1.6 to obtain the required strengths.
C.3 Calculation of Available Strengths The available strengths of members and connections shall be determined in accordance with the provisions of Chapters D, E, F, G, H, and J. The effective length factor k of all members shall be taken as 1. Bracing intended to define the unbraced length of members shall have sufficient stiffness and strength to control member movement at the brace points.
I-39
Chapter D Design of Members for Tension This chapter addresses members subjected to axial tension through the centroidal axis.
D.3 Area Determination
D.1 General Provisions
The net area An of a member is the sum of the products of the thickness and the least net width of each element computed as follows:
The design tensile strength ft Pn and the allowable tensile strength Pn /Wt of tension members shall be determined in accordance with chapter D where
Limit State
ft building-type structures
Wt building-type structures
Wt bridge-type structures
0.75
1.95
2.20
0.90
1.65
1.85
tensile rupture tensile yielding
D.2 Tensile Strength The nominal tensile strength Pn of tension members shall be determined as follows. a) For tensile yielding in the gross section: For unwelded members and members with transverse welds Pn = Fty Ag
(D.2-1)
For members with longitudinal welds Pn = Fty(Ag - Awz) + Ftyw Awz
(D.2-2)
b) For tensile rupture in the net section:
(D.2-3)
(D.2-4)
Block shear rupture strength for the end connections of tension members is given in Section J.6.3.
I-40
s = longitudinal center-to-center spacing (pitch) of any two consecutive holes g = transverse center-to-center spacing (gage) between fastener gage lines For angles, the gage for holes in opposite legs shall be the sum of the gages from the back of the angles less the thickness. Weld metal in plug or slot welds shall not be included in the net area.
D.3.2 Effective Net Area The effective net area Ae for angles, channels, tees, zees, and I-shaped sections shall be determined as follows: a) If tension is transmitted directly to each of the crosssectional elements of the member by fasteners or welds, the effective net area Ae is the net area. b) If tension is transmitted by fasteners or welds through some but not all of the cross-sectional elements of the member, the effective net area Ae is:
( )( )
For welded members Pn = Ftu(Ae - Awz)/kt + Ftuw Awz
The width of holes shall be taken as the nominal hole diameter for drilled or reamed holes and the nominal hole diameter plus 1⁄32 in. (0.8 mm) for punched holes. For a chain of holes extending across a part in any diagonal or zigzag line, the net width of the part shall be obtained by deducting from the gross width the sum of the hole widths of all holes in the chain, and adding, for each gage space in the chain, the quantity s2/4g where
_ _ x y A = A 1 - __ __ 1e n LC LC
For unwelded members Pn = Ftu Ae /kt
D.3.1 Net Area
(D.3-1)
where An = net area of the member at the connection LC = length of the connection in the direction of load, measured from the center of fasteners or the end of welds. If the length of the connection LC is zero, the net effective area is the net area of the connected elements. x– = eccentricity of the connection in the x-axis direction y– = eccentricity of the connection in the y-axis direction
January 2010
Chapter E Design of Members for Compression This chapter addresses members subjected to axial compression through the centroidal axis.
where Fe is the elastic buckling stress determined as follows: a) For doubly symmetric members:
E.1 General Provisions The design compressive strength fc Pn and the allowable compressive strength Pn /Wc are the least value for the limit states of member buckling (E.3), local buckling (E.4), and the interaction between member buckling and local buckling (E.5), where
)
(E.3-6)
b) For singly symmetric members where y is the axis of symmetry:
( )[ √
fc = 0.90 (LRFD) Wc = 1.65 (ASD building-type structures) Wc = 1.85 (ASD bridge-type structures)
]
Fey + F 4FeyFezH ez F = _____ __ 1 - 1 - ________2 e 2H (Fey + Fez)
Buckling constants are given in Tables B.4.1, B.4.2, and B.4.3. For weld-affected members see Section E.6.
E.2 Effective Length The effective length factor k for calculating column slenderness kL/r shall be determined in accordance with Section C.3.
The nominal member buckling strength Pn is
(Fe - Fex)(Fe - Fey)(Fe - Fez) - F e2 (Fe - Fey)(xo /ro)2 - F e2 (Fe - Fex)(yo/ro)2 = 0 (E.3-8) where
2
(E.3-1)
where
(E.3-9)
2
xo + yo H = 1 - ______ r o2
(E.3-10)
p E Fex = ______2 kx L x ____ rx 2
for kL /r < S2, Fc = 0.85(Bc - Dc kL /r) ≤ Fcy
(E.3-2)
for kL /r ≥ S2, Fc = 0.85 π2 E __ 2 kL r
(E.3-3)
( )
kL/r = greatest column slenderness determined from Sections E.3.1 and E.3.2. S2 = Cc
(E.3-4)
E.3.1 Flexural Buckling For flexural buckling, kL/r is the largest slenderness ratio of the column.
(E.3-7)
c) For unsymmetric members, Fe is the lowest root of the cubic equation:
Ix + Iy r o2 = xo2 + yo2 + _____ Ag
E.3 Member Buckling
Pn = Fc Ag
(
p2ECw 1 F = _____ + GJ _____ e (kzLz)2 Ix + Iy
(E.3-11)
( )
p E Fey = ______2 ky L y ____ ry 2
( ) (
(E.3-12)
)
1 p2EC ___ ___w Fez = ____ 2 GJ + Agr o (kzLz)2
(E.3-13)
Ix, Iy = moments of inertia about the principal axes xo, yo = coordinates of the shear center with respect to the centroid ro = polar radius of gyration about the shear center rx, ry = radii of gyration about the centroidal principal axes
E.3.2 Torsional and Flexural-Torsional Buckling For torsional or flexural-torsional buckling, kL/r is the larger of the slenderness ratio for flexural buckling and the equivalent slenderness ratio determined as follows:
( )
___
√
kL = π ___ __ E r e Fe
January 2010
(E.3-5)
E.4 Local Buckling For members without welds, the local buckling strength shall be determined in accordance with either Section E.4.1 or E.4.2. For members with welds, the local buckling strength shall be determined in accordance with Section E.4.1. I-41
E.4.1 Weighted Average Local Buckling Strength The weighted average local buckling strength is
(
n
Pn =
ΣF i=1
ci Ai + Fcy Ag -
n
ΣA i=1
)
i
E.6.1 Compression Members with Transverse Welds (E.4-1)
where Fci = local buckling stress of element i computed per Sections B.5.4.1 through B.5.4.5. Ai = area of element i
E.4.2 Alternate Local Buckling Strength As an alternate to Section E.4.1, the local buckling strength of a shape composed of flat elements may be determined as: Pn = Fc Ag
(E.4-2)
where Fc is determined in accordance with Section B.5.4.6.
E.5 Interaction Between Member Buckling and Local Buckling If the elastic local buckling stress Fe is less than the member buckling stress Fc, the nominal compressive strength of the member shall not exceed
[
2
P = 0.85p ______E_ n (kL/r)2
]
1/3
F e2/3Ag
(E.5-1)
If the local buckling strength is determined from Section E.4.1, Fe is the smallest elastic local buckling stress for all elements of the cross section according to Table B.5.1. If the local buckling strength is determined from Section E.4.2, Fe is the elastic local buckling stress of the cross section determined by analysis.
I-42
E.6 Welded Compression Members
The nominal member buckling strength of a member supported at both ends with no transverse weld farther than 0.05L from the member ends shall be calculated as if there were no welds. The nominal member buckling strength of a member supported at both ends with a transverse weld farther than 0.05L from the member ends and a member supported at only one end with a transverse weld shall be calculated as if the entire cross sectional area were weld-affected. For tubes with circumferential welds, Section B.5.4.5 only applies if Rb /t ≤ 20.
E.6.2 Compression Members with Longitudinal Welds The nominal member buckling strength Pn of members with longitudinal welds is Pn = Pno (1 - Awz /Ag) + Pnw (Awz /Ag)
(E.6-1)
where Pno = nominal member buckling strength if no part of the cross section were weld-affected. Use buckling constants for unwelded metal (Table B.4.1 or Table B.4.2) and mechanical properties from Table A.3.4 or Table A.3.4M. Pnw = nominal member buckling strength if the entire cross section were weld-affected. Use buckling constants for weld-affected zones (Table B.4.1) and mechanical properties from Table A.3.5 or Table A.3.5M.
January 2010
Chapter F Design of Members for Flexure This chapter addresses members subjected to bending that are either a) loaded in a plane parallel to a principal axis that passes through the shear center, or b) restrained against rotation about their longitudinal axis at load points and supports.
F.1 General Provisions The design flexural strength fb Mn and allowable flexural strength Mn /Wb shall be determined in accordance with Chapter F, where Mn = nominal flexural strength, and
Limit State tensile rupture other flexural limit states
fb Wb Wb building-type building-type bridge-type structures structures structures
F.1.1.2 Singly Symmetric Shapes For singly symmetric shapes between brace points a) If Icy /Iy ≤ 0.1 or Icy /Iy ≥ 0.9, Cb = 1.0 b) If 0.1 < Icy /Iy < 0.9, Cb shall be determined using Equation F.1-1. If Mmax produces compression on the larger flange and the smaller flange is also subjected to compression in the unbraced length, the member shall be checked at the location of Mmax using Cb determined using Equation F.1-1 and at the location where the smaller flange is subjected to its maximum compression using Cb = 1.67.
F.2 Open Shapes
Buckling constants are given in Tables B.4.1, B.4.2, and B.4.3. For weld-affected members see Section F.9.
For open shapes subject to lateral-torsional buckling, the nominal flexural strength shall be determined using Sections F.2.1, F.2.3, and F.8. For open shapes not subject to lateral-torsional buckling, the nominal flexural strength shall be determined using Section F.8. For single angles, the nominal flexural strength shall be determined using Section F.5.
F.1.1 Bending Coefficient Cb
F.2.1 Lateral-Torsional Buckling
a) Members supported on both ends: For members subjected to uniform bending moment, the bending coefficient Cb = 1. For other members, Cb shall be taken as 1 or determined in accordance with Section F.1.1.1 or F.1.1.2. b) Cantilevers: Cb shall be determined in accordance with Section F.1.1.1.
For the limit state of lateral-torsional buckling, the nominal flexural strength is Mn = Fb Sc where the lateral-torsional buckling stress Fb is:
F.1.1.1 Doubly Symmetric Shapes
inelastic buckling elastic buckling
0.75
1.95
2.20
0.90
1.65
1.85
For doubly symmetric shapes between brace points 12.5Mmax C = _______________________ b 2.5Mmax + 3MA + 4MB + 3MC
(F.1-1)
Lb__ ______ rye √Cb
Slenderness Limits
Dc L___ b__ Bc - ______ 1.2rye √Cb
Lb__ < S ______ 2 rye √Cb
S2 = 1.2Cc
p2E __________ ______ Lb___ __ 2 1.2rye √Cb
Lb__ ≥ S ______ 2 rye √Cb
Limit State
Fb
(
)
where Mmax = absolute value of the maximum moment in the unbraced segment MA = absolute value of the moment at the quarter point of the unbraced segment MB = absolute value of the moment at the midpoint of the unbraced segment MC = absolute value of the moment at the three-quarter point of the unbraced segment For doubly symmetric shape cantilevers unbraced at the free end, Cb shall be determined as follows: Loading
Cb
Concentrated load applied at the centroid at the free end 1.3 Uniform transverse load applied at the centroid 2.1 January 2010
rye shall be ry or determined from Section F.2.2.
F.2.2 Effective Radius of Gyration rye F.2.2.1 Shapes Symmetric About the Bending Axis For shapes symmetric about the bending axis: a) Between brace points of beams subjected to end moment only or to transverse loads applied at the beam’s neutral axis, or at brace points: _________________ _____________
√ √
( )
y d L 2 1 I___ __ r ye= ___ 1 + 0.152 IJ __ b 1.7 S c y d
(F.2-1)
b) Between brace points of beams subjected to transverse loads applied on the top or bottom flange (where the I-43
load is free to move laterally with the beam if the beam buckles): ____________________________ ________________
√ [
( )]
y d J L__ b 2 1 I___ __ r ye= ___ ±0.5 + 1.25 + 0.152 (F.2-2) 1.7 S c I y d
√
0.5 is negative when the load acts toward the shear center and positive when the load acts away from the shear center. where The y-axis is the centroidal symmetry or principal axis that is parallel to the web. Iy = moment of inertia about the y-axis Sc = section modulus, compression side d = depth of the beam
C1 and C2: if the moment varies linearly between the ends of the unbraced segment C1 = 0 and C2 = 1. For simply supported singly symmetric shapes with 0.1 < Icy /Iy < 0.9: a) For a uniformly distributed load over the entire span, Cb = 1.13, C1 = 0.41Cb, and C2 = 0.47Cb. b) For a concentrated load at a distance aL from one end of the span, Cb = 1.75 - 1.6a(1 - a) C1 = Cbsin2pa/[a(1 - a)p2] C2 = (Cb - C1)/2 c) For two symmetric concentrated loads at a distance aL from each end of the span, Cb = 1 + 2.8a3 C1 = 2Cbsin2pa/(ap2) C2 = (1 - a)Cb - C1/2 g0 = distance from the shear center to the point of application of the load; g0 is positive when the load acts away from the shear center and negative when the load acts towards the shear center. If there is no transverse load (pure moment cases) g0 = 0.
F.2.2.2 Singly Symmetric Shapes Unsymmetric about the Bending Axis For singly symmetric shapes unsymmetric about the bending axis, calculate rye by either: a) using Section F.2.2.1 with Iy, Sc and J determined as though both flanges were the same as the compression flange with the overall depth d remaining the same, or b) using Section F.2.2.3.
Alternately, for singly symmetric I shapes where the smaller flange area is not less than 80% of the larger flange area, j shall be taken as -yo.
where
[
√
__________
( )] F ey
(F.2-4)
π E F ey= _____ k y L b 2 _____ r y
( )
(F.2-5)
I-44
)
(F.2-9)
Lz = unbraced length for twisting kz = effective length factor for torsional buckling ______________
r o = √r x2 + r y2 + x o2 + y o2
(F.2-10)
ky = effective length factor for the compression flange about the y-axis. ky shall not be less than 1.0. U = C1g0 - C2 j
(
2 EC w 1 GJ + π______ F ez = _____ ( k zL z )2 A gr o2
The y-axis is the centroidal symmetry or principal axis such that the tension flange has a positive y coordinate and bending is about the x-axis. The origin of the coordinate system is the intersection of the principal axes. 2
(F.2-8)
Icy = moment of inertia of the compression flange about the y-axis df = the distance between the flange centroids; for tees df is the distance between the flange centroid and the tip of the stem.
(F.2-3)
M e= A gF ey U + U 2+ ro2 ___ F ez
(F.2-7)
where
___
√
)[ ( ) ]
(
2I cy I__ y 2 j = 0.45d f ___ 1 1 I x I y
For shapes unsymmetric about the bending axis and with:
b M L e r ye= ____ ___ S c 1.2π E
)
∫
For singly symmetric I shapes, as an alternative to Equation F.2-7,
F.2.2.3 Shapes Unsymmetric about the Bending Axis
a) braces on both ends, and b) loading that does not cause torsion or lateral bending (if the loading causes torsion or lateral bending, apply Section H.3):
(∫
1 y 3dA+ y x2dA - y j = ___ 0 2I x A A
(F.2-6)
= polar radius of gyration of the cross section about the shear center rx , ry = radii of gyration of the cross section about the centroidal principal axes xo = the shear center’s x-coordinate yo = the shear center’s y-coordinate January 2010
F.2.3 Interaction Between Local Buckling and Lateral-Torsional Buckling
F.4.2 Lateral-Torsional Buckling For the limit state of lateral-torsional buckling with major axis bending, the nominal flexural strength Mn = Fb S where the lateral-torsional buckling stress Fb is:
For open shapes: a) whose flanges are flat elements supported on one edge and b) for which the flange’s elastic buckling stress Fe given in Section B.5.6 is less than the lateral-torsional buckling stress of the beam Fb determined in accordance with Section F.2.1, the lateral-torsional buckling strength shall not exceed
[(
]
π E M n= ________ F e2/3 S c 2 _________ L b ___ 1.2r ye√C b 1/3
2
)
(F.2-11)
_____
( )( )
The nominal flexural strength of pipes and round tubes shall be determined using Section F.6. For other closed shapes, the nominal flexural strength shall be determined using Section F.8. For other closed shapes subject to lateraltorsional buckling, the nominal flexural strength shall not exceed the value determined in Section F.3.1.
2
S2 = Cbr /2.3
b
b
2
b
F.5 Single Angles
a) For the limit state of local buckling: (1) If a leg tip is a point of maximum compression (Figure F.5.1):
Figure F.5.1
F.3.1 Lateral-Torsional Buckling For the limit state of lateral-torsional buckling, the nominal flexural strength is Mn = Fb Sc where the lateral-torsional buckling stress Fb is: Slenderness 2L bS___ c ______ C b√I y J Limits
Limit State Fb ______ inelastic S c 2______ L S c C 2 2L b___ B c- 1.6D c ______ b ___ < S 2 S 2= ___c 1.6 buckling C b√I y J C b√I y J 2 elastic π E 2L b S___ c __________ ______ ≥ S 2 2 S c buckling C b√I y J 2.56 _______ L b____ C b√ I y J
(
b
Slenderness Limits
For single angles, the nominal flexural strength Mn shall be determined as follows.
F.3 Closed Shapes
( )
√
√ _____ L ____ < S √_____ C d L ≥ S √ ____ C d
Limit State Fb ____ inelastic L b d br- 2.3D br d__t ___ B __ C b d t buckling elastic π2E ___________ d__t d 2 ____ buckling 5.29 ___ L b t C bd
√
L b __ dt ____ b d C
)
for b/t ≤ S1, Mn = 1.3FcySc
(F.5-1)
for S1 < b/t < S2, Mn = [Bbr - 4.0Dbr(b/t)]Sc (F.5-2) for b/t ≥ S2, Mn = p2ESc /(4.0(b/t))2
(F.5-3)
where S1 = (Bbr - 1.3Fcy)/(4.0Dbr)
(F.5-4)
S2 = Cbr/4.0
(F.5-5)
(2) If a leg is in uniform compression (Figure F.5.2):
F.4 Rectangular Bars The nominal flexural strength of rectangular bars shall be determined for the limit states of yielding and rupture in Section F.4.1 and lateral-torsional buckling in Section F.4.2.
Figure F.5.2 for b/t ≤ S1, Mn = FcySc
(F.5-6)
F.4.1 Yielding and Rupture
for S1 < b/t < S2, Mn = [Bp - 5.0Dp(b/t)]Sc
(F.5-7)
For the limit state of compressive yielding the nominal flexural strength Mn = 1.3 Fcy S. For the limit state of tensile yielding the nominal flexural strength Mn = 1.3 Fty S. For the limit state of tensile rupture, the nominal flexural strength Mn = 1.42 Ftu S/kt.
for b/t ≥ S2, Mn = p2ESc /(5.0(b/t))2
(F.5-8)
January 2010
where S1 = (Bp - Fcy)/(5.0Dp) S2 = Cp /5.0
(F.5-9) (F.5-10) I-45
b) For the limit state of yielding (Figure F.5.3):
c) Equal leg angles without lateral-torsional restraint: Strengths shall be calculated with Sc equal to 0.80 of the geometric section modulus. If the leg tip is in compression, Mn is the lesser of: (1) local buckling strength determined by Section F.5a(1) (2) lateral-torsional buckling strength determined by F.5c with
Figure F.5.3 Mn = 1.3My
(F.5-11)
where My = yield moment about the axis of bending.
[
______________
]
0.66Eb4tC b 2 M e= _________ √ 1 + 0.78( L b t/b2 ) - 1 (F.5-16) L b2
(F.5-12)
If the leg tip is in tension, Mn is the lesser of: (1) yield strength determined by Section F.5b (2) lateral-torsional buckling strength determined by Section F.5c with
(2) for Me > My, Mn = (1.92 - 1.17√ My/M e )My ≤ 1.3My (F.5-13)
0.66Eb4tC b 2 M e= _________ √ 1 + 0.78( L b t/b2 ) + 1 (F.5-17) L b2
where Me = elastic lateral-torsional buckling moment from Section F.5.1 or F.5.2. Cb between brace points shall be determined using Equation F.1-1 but shall not exceed 1.5.
d) Unequal leg angles without lateral-torsional restraint: moments about the geometric axes shall be resolved into moments about the principal axes and the angle shall be designed as an angle bent about a principal axis (Section F.5.2).
F.5.1 Bending About Geometric Axes
F.5.2 Bending About Principal Axes
c) For the limit state of lateral-torsional buckling: (1) for Me ≤ My, Mn = (0.92 - 0.17Me /My)Me ______
Bending about a geometric axis is shown in Figure F.5.4. For combined axial compression and bending, resolve moments about principal axes and use Section F.5.2.
[
______________
Bending about principal axes is shown in Figure F.5.5.
Minor Axis Bending Subsections (a) and (b)
Subsection (c)
Figure F.5.4 a) Angles with continuous lateral-torsional restraint: Mn is the lesser of: (1) local buckling strength determined by Section F.5a. (2) yield strength determined by Section F.5b. b) Equal leg angles with lateral-torsional restraint only at the point of maximum moment: Strengths shall be calculated with Sc being the geometric section modulus. Mn is the least of: (1) local buckling strength determined by Section F.5a. (2) yield strength determined by Section F.5b. (3) If the leg tip is in compression, lateral-torsional buckling strength determined by Section F.5c with
[
______________
]
0.82Eb4tC b 2 M e= _________ √1 + 0.78( L b t/b2 ) - 1 (F.5-14) L b2 If the leg tip is in tension, lateral-torsional buckling strength determined by Section F.5c with
[
______________
]
0 .82Eb4tC b 2 M e= _________ √1 + 0.78( L b t/b2 ) + 1 (F.5-15) L b2 I-46
]
Major Axis Bending
Figure F.5.5 a) Equal leg angles, major axis bending: Mn is the lesser of: (1) local buckling strength determined by Section F.5a (2) lateral-torsional buckling strength determined by Section F.5c, with 0.46Eb2t2 M e= Cb ________ L b
(F.5-18)
b) Unequal leg angles, major axis bending: Mn is the lesser of: (1) local buckling strength determined by Section F.5a for the leg with its tip in compression (2) lateral-torsional buckling strength determined by Section F.5c, with ________________ I M e= 4.9E ___z2 C b √b w2 + 0.052( L bt/r z )2 + b w L b (F.5-19)
[
]
Iz = moment of inertia about the minor principal axis rz = radius of gyration about the minor principal axis
[
∫
]
1 ( 2 2) b w = __ I w z w + z dA - 2z o,
(F.5-20) January 2010
bw is a section property for unequal leg angles and is positive when the short leg is in compression and negative when the long leg is in compression. (See the commentary for values for common angle sizes and equations for determining bw.) If the long leg is in compression anywhere along the unbraced length of the angle, bw is negative. zo = coordinate along the z-axis of the shear center with respect to the centroid Iw = moment of inertia about the major principal axis c) Equal and unequal leg angles, minor axis bending: (1) If the leg tips are in compression, Mn is the lesser of the local buckling strength determined by Section F.5a(1) and the yield strength determined by Section F.5b. (2) If the leg tips are in tension, Mn is the yield strength determined by Section F.5b.
F.6 Pipes and Round Tubes The nominal flexural strength of pipes and round tubes shall be determined for the limit states of yielding and rupture in Section F.6.1 and local buckling in Section F.6.2.
F.6.1 Yielding and Rupture For the limit state of compressive yielding the nominal flexural strength Mn = 1.17 Fcy S. For the limit state of tensile yielding the nominal flexural strength Mn = 1.17 Fty S. For the limit state of tensile rupture the nominal flexural strength Mn = 1.24 Ftu S/kt.
F.6.2 Local Buckling For the limit state of local buckling, the nominal flexural strength Mn = Fb S where the local buckling stress Fb is: Rb __ t
Slenderness Limits
Limit State Fb ___ upper Btb - Bt 2 R b __ Rb _______ inelastic B tb- D tb __ t t ≤ S1 S 1 = Dtb - Dt buckling ___ lower R b Rb inelastic B t- D t __ S 1 < __ t t < S2 buckling elastic Rb π2E _______________ _____ 2 __ S2 = Ct buckling R t ≥ S2 R b / t 16 __ b 1 + √_____ t 35
(
√
)
√
( )(
)
F.7 Rods For rods, the nominal flexural strength shall be determined for the limit states of yielding and tensile rupture. For the limit state of yielding, the nominal flexural strength Mn is the lesser of 1.3Fty S and 1.3Fcy S. For the limit state of tensile rupture, the nominal flexural strength Mn = 1.42Ftu S /kt. January 2010
F.8 Elements of Flexural Members The nominal flexural strength of the elements of flexural members is the least of the strengths for tensile yielding and tensile rupture or for compression yielding and local buckling. Alternately, the nominal flexural strength of the elements of flexural members shall be determined as the weighted average flexural strength using Section F.8.3. For the limit states of yielding and tensile rupture, the nominal flexural strength is Mn = Fb St where Fb is determined using Section F.8.1. For the limit state of compression, the nominal flexural strength is Mn = Fb Sc where Fb is determined using Section F.8.2.
F.8.1 Tension F.8.1.1 Elements in Uniform Tension For the limit state of tensile yielding, the flexural tensile stress corresponding to the nominal flexural strength is: For unwelded elements: Ft = Fty For transversely welded elements: Ft = Ftyw For longitudinally welded elements: Ft = Fty(1 - Awz /Ag) + Ftyw Awz /Ag For the limit state of tensile rupture, the flexural tensile stress corresponding to the nominal flexural strength is: For unwelded elements: Ft = Ftu/kt For transversely welded elements: Ft = Ftuw For longitudinally welded elements: Ft = Ftu(1 - Awz /Ag)/kt + Ftuw Awz /Ag. F.8.1.2 Elements in Flexure For the limit state of tensile yielding, the flexural tensile stress corresponding to the nominal flexural strength is: For unwelded elements: Fb = 1.30 Fty For transversely welded elements: Fb = 1.30 Ftyw For longitudinally welded elements: Fb = 1.30[Fty(1 - Awzt /Agt) + Ftyw Awzt /Agt] For the limit state of tensile rupture, the flexural tensile stress corresponding to the nominal flexural strength is: For unwelded elements: Fb = 1.42Ftu/kt For transversely welded elements: Fb = 1.42Ftuw For longitudinally welded elements: Fb = 1.42[Ftu(1 - Awzt /Agt)/kt + Ftuw Awzt /Agt]
F.8.2 Compression For elements in compression, the flexural compressive stress corresponding to the nominal flexural strength Fb is given in Sections F.8.2.1 and F.8.2.2. Alternately, the compressive strength of elements of beams composed of flat elements may be determined using Section F.8.2.3. I-47
F.8.2.1 Elements in Uniform Compression For beam elements in uniform compression, the flexural compressive strength is given in Section B.5.4. F.8.2.2 Elements in Flexure For beam elements in flexure, the flexural compressive strength is given in Section B.5.5. F.8.2.3 Alternate Compressive Flexural Strength As an alternate to Sections F.8.2.1 and F.8.2.2, the compressive strength of elements of beams composed of flat elements without welds may be determined as follows: The flexural compressive stress Fc corresponding to the nominal flexural strength for the shape’s flat elements in uniform compression shall be determined in accordance with Section B.5.4.6. The flexural compressive stress Fb corresponding to the nominal flexural strength for the shape’s flat elements in flexure shall be determined in accordance with Section B.5.5.4.
If there are stiffeners located farther than the compression flange from the cross section’s neutral axis, the compressive flexural strength shall not exceed Fcy If /ccs + Fb Iw /ccw where
F.8.3 Weighted Average Flexural Strength The weighted average nominal flexural strength Mn is the lesser of
ccs = distance from the cross section’s neutral axis to the extreme fiber of compression flange stiffeners and b) the tensile flexural strength
a) the compressive flexural strength M nc= F cI f/c cf+ F b I w /c cw
Fb = local buckling stress of the flat elements in flexure determined using Section F.8.2.2 or F.8.2.3. ccf = distance from the centerline of the compression flange to the cross section’s neutral axis ccw = distance from the web group’s extreme compression fiber to the cross section’s neutral axis If = moment of inertia of the flange group about the cross section’s neutral axis. The flange group consists of the flat elements in uniform compression and the flat elements in uniform tension and their edge or intermediate stiffeners. Iw = moment of inertia of the web group about the cross section’s neutral axis. The web group consists of the flat elements in flexure and their intermediate stiffeners.
(F.8-1)
where (see Figure F.8.1) Fc = local buckling stress of the flat elements in uniform compression determined using Section F.8.2.1 or F.8.2.3. The strength of stiffened elements shall not exceed the strength of an intermediate stiffener or an edge stiffener.
M nt= F t I f/c tf+ F bIw /c tw
(F.8-2)
where (see Figure F.8.1) Ft = tensile stress for the flat elements in uniform tension determined using Section F.8.1.1 Fb = tensile stress for the flat elements in flexure determined using Section F.8.1.2
Figure F.8.1 I-48
January 2010
ctf = distance from the extreme tension fiber to the cross section’s neutral axis ctw = distance from the web group’s extreme tension fiber to the cross section’s neutral axis
F.9 Welded Flexural Members F.9.1 Flexural Members with Transverse Welds The lateral-torsional buckling strength of members supported at both ends with no transverse weld farther than 0.05L from the member ends shall be calculated as if there were no welds. The lateral-torsional buckling strength of members supported at both ends with a transverse weld farther than 0.05L from the member ends and members supported at only one end with a transverse weld at any location shall be calculated as if the entire cross-sectional area were weldaffected. For tubes with circumferential welds, Section B.5.4.5 only applies if Rb /t ≤ 20.
January 2010
F.9.2 Flexural Members with Longitudinal Welds The lateral-torsional buckling strength Mn of members with longitudinal welds is Mn = Mno(1 - Awz/Af) + Mnw(Awz/Af)
(F.9-1)
where Mno = lateral-torsional buckling strength if no part of the cross section were weld-affected. Use buckling constants for unwelded metal (Table B.4.1 or Table B.4.2) and mechanical properties from Table A.3.4 or Table A.3.4M. Mnw = lateral-torsional buckling strength if the entire cross section were weld-affected. Use buckling constants for weld-affected zones (Table B.4.1) and mechanical properties from Table A.3.5 or Table A.3.5M. Af = area of the member farther than 2c/3 from the neutral axis, where c is the distance from the neutral axis to the extreme compression fiber.
I-49
Chapter G Design of Members for Shear This chapter addresses flat webs of members subjected to shear in the plane of the web and shear in round and oval tubes.
G.1 General Provisions The design shear strength fvVn and the allowable shear strength Vn /Wv shall be determined from Section G.2 or G.3, where fv = 0.90 (LRFD) Wv = 1.65 (ASD building-type structures) Wv = 1.85 (ASD bridge-type structures) The shear stress corresponding to the shear strength is For unwelded members: Fs = Fso
(G.1-1)
For welded members: Fs = Fso(1 - Awz/Ag) + Fsw Awz /Ag
(G.1-2)
where Fso = shear stress corresponding to the shear strength for an element if no part of the cross section were weld-affected. Use buckling constants for unwelded metal (Table B.4.1 or Table B.4.2) and mechanical properties from Table A.3.4 or Table A.3.4M. Fsw = shear stress corresponding to the shear strength for an element if the entire cross section were weld-affected. Use buckling constants for weldaffected zones (Table B.4.1) and mechanical properties from Table A.3.5 or Table A.3.5M. For transversely welded elements with b/t ≤ S1, Fs = Fso. Awz = cross sectional area of the weld-affected zone Ag = gross cross sectional area of the element.
The shear stress Fs corresponding to the shear strength is
Limit State
Fs
b/t
yielding
Fsy
b/t ≤ S1
inelastic buckling
Bs - 1.25Ds b/t
S1 < b/t < S2
elastic buckling
p2E ________ (1.25b/t)2
b/t ≥ S2
Slenderness Limits Bs - Fsy S1 = _______ 1.25Ds
Cs S2 = ____ 1.25
where b = clear height of the web (see Figure G.2.1) for unstiffened webs and ___________ 1 ____a____ ___ for webs with transverse stiffeners b = __ 1 + 0.7 a1 2 a2 a1 = the lesser of the clear height of the web and the distance between stiffeners a2 = the greater of the clear height of the web and the distance between stiffeners t = web thickness Aw = dt d = full depth of the section
√
()
Transverse stiffeners shall have a moment of inertia Is not less than the following:
() ()
s 0.55Vb2 s __ ≤ 0.4, Is = _______ __ b E b
(G.2-2)
0.088Vb_ 2 _b_ _s_ > 0.4, I = _______ s b E s
(G.2-3)
The shear stress Fs corresponding to the nominal shear strength in weld-affected zones shall not exceed Fsuw /1.2.
G.2 Members with Flat Webs Supported on Both Edges The nominal shear strength Vn of flat webs supported on both edges is Vn = Fs Aw
I-50
(G.2-1)
Figure G.2.1 FLAT WEBS IN SHEAR
January 2010
where b = clear height of the web regardless of whether or not a longitudinal stiffener is present Is = moment of inertia of the transverse stiffener. For a stiffener composed of members of equal size on each side of the web, the moment of inertia of the stiffener shall be computed about the centerline of the web. For a stiffener composed of a member on only one side of the web, the moment of inertia of the stiffener shall be computed about the face of the web in contact with the stiffener. s = transverse stiffener spacing. For a stiffener composed of a pair of members, one on each side of the web, the stiffener spacing s is the clear distance between the pairs of stiffeners. For a stiffener composed of a member on only one side of the web, the stiffener spacing s is the distance between fastener lines or other connecting lines. V = shear force on the web at the transverse stiffener Stiffeners shall extend from flange to flange but need not be connected to either flange. Unless the outer edge of a stiffener is continuously stiffened, its thickness shall not be less than 1⁄12th the clear width of the outstanding leg.
January 2010
G.3 Round or Oval Tubes The nominal shear strength Vn of round or oval tubes is Vn = Fs Ag /2
(G.3-1)
where: Limit State
Fs
lt
yielding
Fsy
l t ≤ S1
inelastic buckling
1.3Bs - 1.63Ds l t
S1 < l t < S2
elastic buckling
1.3p2E _________ (1.25 l t)2
l t ≥ S2
( )( )
Rb 5/8 __ L_v 1/4 l = 2.9 __ t t Rb
Slenderness Limits 1.3Bs - F_sy ________ S1 = 1.63Ds
Cs_ S = ___ 2 1.25
(G.3-2)
Rb = mid-thickness radius of a round tube or maximum mid-thickness radius of an oval tube t = thickness of tube Lv = length of tube from maximum to zero shear force.
I-51
Chapter H Design of Members for Combined Forces and Torsion This chapter addresses members subject to axial force and flexure about one or both axes, with or without torsion, and to members subject to torsion only.
H.1 Members Subject to Flexure and Axial Force For members subject to flexure and axial force,
Pr ___ M M __ + rx + ___ry ≤ 1.0 Pc Mcx Mcy
(H.1-1)
where: x = subscript for major principal axis bending y = subscript for minor principal axis bending For LRFD: Pr = required axial force using LRFD load combinations For axial tension: Pc = design axial tensile strength determined in accordance with Chapter D For axial compression: Pc = design axial compressive strength determined in accordance with Chapter E Mr = required flexural strength using LRFD load combinations Mc = design flexural strength determined in accordance with Chapter F For ASD: Pr = required axial force using ASD load combinations For axial tension: Pc = allowable axial tensile strength determined in accordance with Chapter D For axial compression: Pc = allowable axial compressive strength determined in accordance with Chapter E Mr = required flexural strength using ASD load combinations Mc = allowable flexural strength determined in accordance with Chapter F
H.2 Members Subject to Torsion The design torsional strength fTTn and the allowable torsional strength Tn/WT shall be determined in accordance with Section H.2, where fT = 0.90 (LRFD) WT = 1.65 (ASD building-type structures) WT = 1.85 (ASD bridge-type structures)
H.2.1 Round or Oval Tubes The nominal torsional strength Tn for round or oval tubes for the limit state of torsional yielding and torsional buckling is I-52
Tn = Fs J/R
(H.2-1)
where
Limit State
Fs
lt
yielding
Fsy
lt ≤ S1
inelastic buckling
Bs - 1.25Ds lt
S1 < lt < S2
elastic buckling
p2E _______ (1.25l t)2
lt ≥ S2
()( )
Rb 5/8 ___ Ls 1/4 l = 2.9 __ t t Rb
Slenderness Limits Bs - Fsy S1 = _______ 1.25Ds
Cs S2 = ____ 1.25 (H.2-2)
Rb = mid-thickness radius of a round tube or the maximum mid-thickness radius of an oval tube t = tube thickness Ls = length of tube between circumferential stiffeners, or overall length if no circumferential stiffeners are present R = outside radius of the tube J = torsion constant of the tube
H.2.2 Rectangular Tubes The nominal torsional strength Tn for rectangular tubes for the limit state of torsional yielding and torsional buckling is Tn = FsC
(H.2-3)
where Fs is determined in accordance with Section G.2 for the side with the larger slenderness and C is the torsional shear constant.
H.2.3 Rods The nominal torsional strength Tn for rods for the limit state of torsional yielding is Tn = 0.196Fsy D3
(H.2-4)
where D = diameter of the rod
H.3 Members Subject to Torsion, Flexure, Shear, and/or Axial Compression H.3.1 Flat Elements Stresses in flat elements subject to torsion, flexure, shear, and/or axial compression shall satisfy the following: For LRFD: fc /(φFc ) + [ fb /(φFb )]2 + [ fs /(φFs )]2 ≤ 1.0
(H.3-1) January 2010
For ASD: fc /(Fc /Ω) + [ fb /(Fb /Ω)]2 + [ fs /(Fs /Ω)]2 ≤ 1.0
For LRFD: (H.3-2)
where fc = uniform compressive stress due to axial compression and bending fb = compressive stress due to flexure fs = shear stress due to shear and torsion Fc = axial compression stress corresponding to the nominal axial compression strength Fb = bending stress corresponding to the nominal flexural compression strength Fs = shear stress corresponding to the nominal shear strength
H.3.2 Curved Elements Stresses in curved elements subject to torsion, flexure, shear, and/or axial compression shall satisfy the following:
January 2010
fc /(φFc ) + fb /(φFb ) + [ fs /(φFs )]2 ≤ 1.0
(H.3-3)
For ASD: fc /(Fc /Ω) + fb /(Fb /Ω) + [ fs /(Fs /Ω)]2 ≤ 1.0
(H.3-4)
where fc = compressive stress due to axial compression fb = compressive stress due to flexure fs = shear stress due to shear and torsion Fc = axial compression stress corresponding to the nominal axial compression strength Fb = bending stress corresponding to the nominal flexural compression strength Fs = shear stress corresponding to the nominal shear strength
I-53
Chapter J Design of Connections This chapter addresses connecting elements and connectors.
J.1 General Provisions J.1.1 Design Basis The design strength and the allowable strength of connections shall be determined in accordance with the provisions of this chapter and Chapter B. If the longitudinal centroidal axes of connected axially loaded members do not intersect at one point, the connection and members shall be designed for the effects of eccentricity.
J.1.2 Fasteners in Combination with Welds Fasteners shall not be considered to share load in combination with welds.
J.1.3 Maximum Spacing of Fasteners The pitch and gage of fasteners joining components of tension members shall not exceed (3 + 20t) in. [(75 + 20t) mm] where t is the thickness of the outside component. In outside components of compression members:
c) Welds welded from one side using AC-GTAW root pass without backing d) Welds welded from one side using PAW-VP in the keyhole mode. All other groove welds are partial penetration welds. J.2.1.2 Effective Area a) Size: The size Sw of a complete joint penetration groove weld is the thickness of the thinner part joined. The size Sw of a partial joint penetration groove weld is the depth of preparation (see Figure J.2.1) for all V and bevel groove welds with an included angle greater than 45°, and the depth of preparation of all J and U groove welds. b) Length: The effective weld length Lwe for tension and compression is the length of the weld perpendicular to the direction of tensile or compressive stress. The effective weld length for shear is the length of the weld parallel to the direction of shear stress. c) Area: The effective area Awe of a groove weld is the effective weld length times the weld size.
a) The component’s strength shall satisfy the requirements of Section E.3 with an effective length kL = s/2, where s is the pitch, and b) If multiple rows of fasteners are used, the component’s strength shall satisfy the requirements of Section B.5.4.2 with a width b = 0.8g where g is the gage. If only one line of fasteners is used, the component’s strength shall satisfy the requirements of Section B.5.4.1 with a width b = the edge distance of the fastener.
J.2 Welds
Figure J.2.1 PARTIAL JOINT PENETRATION GROOVE WELD
The design strength fRn and allowable strength Rn/W of welds shall be determined from Sections J.2.1 through J.2.4 where f = 0.75 (LRFD) W = 1.95 (ASD building-type structures) W = 2.20 (ASD bridge-type structures)
J.2.1.3 Strength
J.2.1 Groove Welds
The nominal tensile or compressive strength Rn of a groove weld is:
J.2.1.1 Complete Penetration and Partial Penetration Groove Welds
Rn = Ftuw Awe
The following types of groove welds are complete penetration welds:
where
a) Welds welded from both sides with the root of the first weld backgouged to sound metal before welding the second side. b) Welds welded from one side using permanent or temporary backing. I-54
(J.2-1)
Ftuw = least of the welded tensile ultimate strengths of the base metals and the filler. Welded tensile ultimate strengths of base metals shall be taken from Table A.3.5 or Table A.3.5M and tensile ultimate strengths of fillers from Table J.2.1 or Table J.2.1M. January 2010
Rn = Fsw Lwe
Awe = weld effective area
The nominal shear strength Rn of a groove weld is: Rn = Fsuw Awe
(J.2-3)
where (J.2-2)
where Fsuw = least of the welded shear ultimate strengths of the base metals and the filler. Welded shear ultimate strengths of base metals shall be taken from Table A.3.5 or Table A.3.5M and shear ultimate strengths of fillers from Table J.2.1 or Table J.2.1M Awe = weld effective area.
J.2.2 Fillet Welds J.2.2.1 Effective Throat and Effective Length a) The effective throat is the shortest distance from the joint root to the face of the diagrammatic weld (see Figure J.2.2).
Fsw = least of: a) the product of the weld filler’s shear ultimate strength and the effective throat. b) for base metal in shear at the weld-base metal joint, the product of the base metal’s welded shear ultimate strength and the fillet size Sw at the joint; c) for base metal in tension at the weld-base metal joint, the product of the base metal’s welded tensile ultimate strength and the fillet size Sw at the joint. Welded shear and tensile ultimate strengths of base metals shall be taken from Table A.3.5 or Table A.3.5M and shear ultimate strengths of weld fillers from Table J.2.1 or Table J.2.1M. Lwe = weld effective length
J.2.3 Plug and Slot Welds J.2.3.1 Effective Area The effective area Awe of plug or slot welds is the nominal area of the hole or slot in the plane of the faying surface (see Figure J.2.3). Slot lengths shall not exceed 10 times the slotted material’s thickness.
Figure J.2.2 EFFECTIVE THROAT OF A FILLET WELD
Figure J.2.3 SLOT WELD PLAN VIEW
b) The weld effective length Lwe is the overall length of the weld, including boxing. If the effective length of a fillet weld is less than 4 times its nominal size Sw (see Figure J.2.2), the effective weld size shall be considered to be 25% of its effective length.
J.2.3.2 Strength
The minimum length of segments of an intermittent fillet weld shall be 1½ in. (40 mm). The maximum effective length of an end-loaded fillet weld is 100Sw.
where
J.2.2.2 Strength Stress on a fillet weld shall be considered to be shear for any direction of applied load. The nominal shear strength Rn of a fillet weld is: January 2010
The nominal shear strength Rn of a plug or slot weld is: Rn = Fsw Awe
(J.2-4)
Fsw = lesser of the welded shear ultimate strengths of the filler and the base metal under the weld. Welded shear ultimate strengths of base metals shall be taken from Table A.3.5 or Table A.3.5M and shear ultimate strengths of fillers from Table J.2.1 or Table J.2.1M. Awe = weld effective area I-55
Table J.2.1 FILLER STRENGTHS Filler
Tensile Ultimate Strength (ksi)
Shear Ultimate Strength (ksi)
1100
11
2319
35
16
4043
24
11.5
4047
–
Table J.2.2 TENSILE STRENGTHS FOR 5183, 5356, AND 5556 STUDS Arc (lb)
Capacitor Discharge (lb)
6–32
–
375
8–32
–
635
13
10–24
770
770
7.5
Stud Size
4643
–
13.5
¼–20
1360
1360
5183
40
21
5
⁄16–18
2300
2300
5356
35
17
3
⁄8–16
3250
–
5554
31
17
7
⁄16–14
4400
–
5556
42
20
½–13
5950
–
5654
30
12
Table J.2.1M FILLER STRENGTHS
Table J.2.2M TENSILE STRENGTHS FOR 5183, 5356, AND 5556 STUDS
Tensile Ultimate Strength (MPa)
Shear Ultimate Strength (MPa)
Stud Size
1100
75
50
6–32
2319
240
110
8–32
4043
165
80
10–24
3.42
3.42
4047
–
90
¼–20
6.05
6.05
4643
–
95
5
⁄16–18
10.2
10.2
5183
275
145
3
⁄8–16
14.5
–
5356
240
115
7
⁄16–14
19.6
–
5554
215
115
½–13
26.5
–
5556
290
140
5654
205
85
Filler
J.2.4 Stud Welds The nominal tensile strength Rn of a stud weld is: Rn = Tuw
(J.2-5)
where Tuw = tensile strength of the stud in Table J.2.2 or Table J.2.2M The base metal thickness for arc stud welding shall not be less than 50% of the stud diameter. The base metal thickness for capacitor discharge stud welding shall not be less than 25% of the stud diameter.
J.2.5 Post-Weld Heat Treating For 6005 lighting poles through 0.250 in. (6 mm) thick welded in the T1 temper with 4043 filler and artificially aged to the T5 temper after welding, design and allowable
I-56
Arc (kN)
Capacitor Discharge (kN)
–
1.67
–
2.82
stresses of the base metal within 1.0 in. (25 mm) of the weld shall be 85% of the values for unwelded 6005-T5. For 6063 lighting poles through 0.375 in. (10 mm) thick welded in the T4 temper with 4043 filler and artificially aged to the T6 temper after welding: a) The design and allowable stresses of the base metal within 1.0 in. (25 mm) of the weld shall be 85% of the values for unwelded 6063-T6. b) The design stress is 12.5 ksi (85 MPa) and the allowable stress is 8 ksi (55 MPa) for welds in socket type bases. c) The design stress is 9 ksi (60 MPa) and the allowable stress is 5.9 ksi (41 MPa) for welds in other than socket type bases.
J.3 Bolts J.3.1 Bolt Material Bolt material shall be: a) Aluminum: Bolts shall meet ASTM F 468 and be 2024T4, 6061-T6, or 7075-T73. When 2024 bolts will be exposed to contact with liquid water or humidity near
January 2010
the dew point in the intended service, they shall have a minimum 0.0002 in. (0.005 mm) thick anodic coating. Nuts shall meet ASTM F 467. Nuts for ¼ in. (M6) bolts and smaller shall be 2024-T4; larger nuts shall be 6061T6 or 6262-T9. Flat washers shall be Alclad 2024-T4. Spring lock washers shall be 7075-T6. b) Carbon steel: Carbon steel bolts, nuts, and washers shall have a hot-dip zinc coating meeting ASTM A 153 or a mechanically deposited zinc coating meeting ASTM B 695 and shall be lubricated in accordance with ASTM A 563. The zinc coating thickness shall be adequate to provide corrosion protection for the anticipated service. If other coatings are used, their thickness shall be sufficient to provide corrosion protection for the intended service. Bolt hardness shall be less than Rockwell C35. A 490 bolts shall not be used. c) Stainless steel: Stainless steel bolts, nuts and washers shall be 300 series. Bolts shall meet ASTM F 593, A 193, or A 320. Nuts shall meet ASTM F 594 or A 194.
where Ftu = tensile ultimate strength of the bolt (Table A.3.8 or Table A.3.8M).
J.3.6 Bolt Shear For aluminum bolts, the design shear strength fRn and the allowable shear strength Rn/W shall be determined for the limit state of shear rupture as follows: f = 0.65 (LRFD) W = 2.34 (ASD building-type structures) W = 2.64 (ASD bridge-type structures) a) For bolts with threads in the shear plane, Rn = (π(D - 1.191/n)2/4)Fsu b) For bolts without threads in the shear plane, Rn = (πD2/4)Fsu
J.3.2 Holes and Slots for Bolts The nominal diameter of holes for bolts shall not be more than 1⁄16 in. (2 mm) greater than the nominal diameter of the bolt unless slip-critical connections are used. The nominal width of slots for bolts shall not be more than 1⁄16 in. (2 mm) greater than the nominal diameter of the bolt. If the nominal length of the slot exceeds 2.5D or the edge distance is less than 2D, where D is the nominal bolt diameter, the edge distance perpendicular to the slot length and slot length shall be sized to avoid overstressing the material along the slot. Unless slip-critical connections are used, the length shall be perpendicular to the direction of force.
(J.3-2)
(J.3-3)
where Fsu = shear ultimate strength of the bolt (Table A.3.8 or Table A.3.8M).
J.3.7 Bolt Bearing The design bearing strength fRn and the allowable bearing strength Rn/W shall be determined for the limit state of bearing as follows: f = 0.75 (LRFD) W = 1.95 (ASD building-type structures) W = 2.20 (ASD bridge-type structures)
J.3.3 Minimum Spacing of Bolts
a) For a bolt in a hole,
The distance between bolt centers shall not be less than 2.5 times the nominal diameter of the bolt.
Rn = detFtu ≤ 2DtFtu
J.3.4 Minimum Edge Distance of Bolts
b) For a bolt in a slot with the slot perpendicular to the direction of force:
The distance from the center of a bolt to an edge of a part shall not be less than 1.5 times the nominal diameter of the bolt. See Section J.3.7 for the effect of edge distance on bearing strength.
J.3.5 Bolt Tension For aluminum bolts, the design tension strength fRn and the allowable tension strength Rn/W shall be determined for the limit state of tensile rupture as follows: f = 0.65 (LRFD) W = 2.34 (ASD building-type structures) W = 2.64 (ASD bridge-type structures) Rn = (π(D - 1.191/n)2/4)Ftu
January 2010
(J.3-1)
Rn = 1.33 DtFtu
(J.3-4)
(J.3-5)
and the edge distance perpendicular to the slot length and slot length shall be sized to avoid overstressing the material between the slot and the edge of the part. where de = distance from the center of the bolt to the edge of the part in the direction of force. t = for plain holes, thickness of the connected part; for countersunk holes, thickness of the connected part less ½ the countersink depth Ftu = tensile ultimate strength of the connected part D = nominal diameter of the bolt
I-57
J.3.8 Slip-Critical Bolted Connections
The design slip resistance fRn and the allowable slip resistance Rn /W shall be determined for the limit state of slip as follows:
J.3.8.1 General Slip-critical connections between aluminum members or between aluminum and steel members shall comply with the Research Council on Structural Connections (RCSC) Specification for Structural Joints Using ASTM A325 or A490 Bolts except as modified here. Slip-critical connections shall be designed for the limit states of shear rupture in accordance with Section J.3.8.4, bearing strength in accordance with Section J.3.7, and slip in accordance with Section J.3.8.5. J.3.8.2 Material Aluminum used in slip-critical connections shall have a tensile yield strength of at least 15 ksi (105 MPa). Bolts shall comply with ASTM A 325, nuts shall comply with ASTM A 563 Grade DH or ASTM A 194 Grade 2H, and washers shall comply with ASTM F 436. Bolts, nuts, and washers shall be zinc coated by the hot-dip or mechanically deposited processes as specified in ASTM A 325. J.3.8.3 Holes Holes shall be standard holes, oversize holes, short slotted holes, or long slotted holes. The nominal dimensions for each hole type shall not exceed those shown in the RCSC specification. J.3.8.4 Design for Strength The design shear strength fRn and the allowable shear strength Rn /W shall be determined for the limit state of shear rupture as follows: f = 0.75 (LRFD) W = 2.0 (ASD building-type structures) W = 2.24 (ASD bridge-type structures) Rn = Fn Ab
(J.3-6)
where Fn = 48 ksi (330 MPa) for bolts with threads in the shear plane Fn = 60 ksi (414 MPa) for bolts without threads in the shear plane Ab = nominal cross sectional area (unthreaded body area) of the bolt J.3.8.5 Design for Slip Resistance Slip-critical connections shall be designed for the limit state of slip as follows: a) connections with standard holes or slots transverse to the direction of the load shall be designed to prevent slip as a serviceability limit state. b) connections with oversized holes or slots parallel to the direction of the load shall be designed to prevent slip as a strength limit state. I-58
Rn = 1.13µhscTbNs
(J.3-7)
For connections in which slip prevention is a serviceability limit state f = 1.00 (LRFD) W = 1.50 (ASD building-type structures) W = 1.68 (ASD bridge-type structures) For connections in which slip prevention is a strength limit state f = 0.85 (LRFD) W = 1.76 (ASD building-type structures) W = 1.97 (ASD bridge-type structures) where µ = mean slip coefficient = 0.50 for aluminum surfaces abrasion blasted with coal slag to SSPC SP-5 to an average substrate profile of 2.0 mils (0.05 mm) in contact with similar aluminum surfaces or zinc painted steel surfaces with a maximum dry film thickness of 4 mils (0.1 mm) (Class B surfaces). Determine slip coefficients for other surfaces in accordance with the RCSC specification Appendix A. hsc = hole factor determined as follows: a) for standard size holes hsc = 1.00 b) for oversized and short-slotted holes hsc = 0.85 c) for long-slotted holes perpendicular to the direction of load hsc = 0.70 d) for long-slotted holes parallel to the direction of load hsc = 0.60 Tb = minimum fastener tension specified in the RCSC specification Table 8.1 Ns = number of slip planes J.3.8.6 Washers Washers shall be used under bolt heads and under nuts. At a long slotted hole in an outer ply, a galvanized steel plate washer or bar at least 5⁄16 in. (8 mm) thick with standard holes, shall be used. The plate washer or bar shall completely cover the slot but need not be hardened. Where the outer face of the bolted parts has a slope greater than 1:20 with respect to a plane normal to the bolt axis, a beveled washer shall be used.
J.3.9 Lockbolts Lockbolts shall meet the requirements in this Specification for conventional bolts and be installed in conformance January 2010
with the lockbolt manufacturer’s specifications. The bearing areas under the head and collar shall not be less than those of a conventional bolt and nut.
J.3.10 Long Grips If the grip (total thickness of parts being fastened) of an aluminum bolt exceeds 4.5D, the bolt’s nominal shear strength shall be reduced by dividing by [½ + Gf /(9D)] where Gf is the grip and D is the bolt’s nominal diameter.
J.4.7 Rivet Bearing The design bearing strength fRn and the allowable bearing strength Rn /W shall be determined for the limit state of bearing as follows: f = 0.75 (LRFD) W = 1.95 (ASD building-type structures) W = 2.20 (ASD bridge-type structures) Rn = detFtu ≤ 2DhtFtu
J.4 Rivets
where
J.4.1 Rivet Material Rivets shall be aluminum meeting ASTM B 316 or 300 series stainless steel. Carbon steel shall not be used unless the aluminum is joined to carbon steel (see Section M.7.1) and corrosion resistance of the structure is not required or the structure is protected against corrosion.
J.4.2 Holes for Cold-Driven Rivets The finished diameter of holes for cold-driven rivets shall not be more than 4% greater than the nominal diameter of the rivet.
J.4.3 Minimum Spacing of Rivets The distance between rivet centers shall not be less than 3 times the nominal diameter of the rivet.
J.4.4 Minimum Edge Distance of Rivets The distance from the center of a rivet to an edge of a part shall not be less than 1.5 times the nominal diameter of the rivet. See Section J.4.7 for the effect of edge distance on the bearing strength.
J.4.5 Rivet Tension Aluminum rivets shall not be used to carry tensile loads.
J.4.6 Rivet Shear For aluminum rivets, the design shear strength fRn and the allowable shear strength Rn /W shall be determined for the limit state of shear rupture as follows: f = 0.65 (LRFD) W = 2.34 (ASD building-type structures) W = 2.64 (ASD bridge-type structures) Rn = πDh2Fsu /4
(J.4-1)
where Dh = nominal diameter of the hole (See Section J.4.2 for hole size limits and Section J.4.9 for hollow-end rivets). Fsu = shear ultimate strength of the rivet (See Table A.3.9 or Table A.3.9M). January 2010
(J.4-2)
de = distance from the center of the rivet to the edge of the part in the direction of force. t = for plain holes, nominal thickness of the connected part; for countersunk holes, nominal thickness of the connected part less ½ the countersink depth Ftu = tensile ultimate strength of the connected part Dh = nominal diameter of the hole
J.4.8 Blind Rivets Grip lengths and hole sizes for blind rivets shall comply with the manufacturer’s specifications.
J.4.9 Hollow-End (Semi-Tubular) Rivets The shear strength of hollow-end rivets with solid cross sections for a portion of the length shall be taken equal to the strength of solid rivets of the same material if the bottom of the cavity is at least 25% of the rivet diameter from the plane of shear.
J.5 Tapping Screws This section applies to tapping screws with a nominal diameter D from 0.164 in. (4.2 mm) (No. 8) through 0.25 in. (6.3 mm). Screws shall be thread-forming or threadcutting, with or without a self-drilling point. Screws shall be installed in accordance with the manufacturer’s specifications.
J.5.1 Screw Material Screws shall be: a) aluminum, b) 300 series stainless steel, or c) if the screw will not be exposed to contact with liquid water or humidity near the dew point in its intended service: 1) 400 series stainless steel with a minimum nominal composition of 16% chromium and a Rockwell hardness less than C35 in the load bearing portion of the shank, or 2) coated carbon steel with a Rockwell hardness less than C35 in the load-bearing portion of the shank. Screws shall be zinc coated per ASTM A 123, A 641, I-59
or B 695 or nickel/chromium plated per ASTM B 456, Type SC. If other coatings are used, their thickness shall be sufficient to provide corrosion protection for the intended service.
J.5.2 Holes for Screws The nominal diameter of unthreaded holes for screws shall not exceed the nominal diameter of the screw by more than 1⁄16 in. (1.6 mm). The nominal diameter of threaded holes for screws shall not exceed that given in Tables J.5.1 and J.5.2.
J.5.3 Minimum Spacing of Screws The distance between screw centers shall not be less than 2.5 times the nominal diameter of the screw.
Table J.5.1 HOLE DIAMETERS FOR TYPE AB, B, AND BP SCREWS Screw Size 8
10
12
¼
Metal Thickness (in.)
Hole Diameter (in.) (note 1)
Drill Size
0.030 0.036 0.048 0.060 0.075 0.105 0.125 0.135 0.162 to 0.375
0.116 0.120 0.128 0.136 0.140 0.147 0.147 0.149 0.152
32 31 30 29 28 26 26 25 24
0.036 0.048 0.060 0.075 0.105 0.125 0.135 0.164 0.200 to 0.375
0.144 0.144 0.144 0.147 0.147 0.154 0.154 0.159 0.166
27 27 27 26 26 23 23 21 19
0.048 0.060 0.075 0.105 0.125 0.135 0.164 0.200 to 0.375
0.161 0.166 0.173 0.180 0.182 0.182 0.189 0.196
20 19 17 15 14 14 12 9
0.060 0.075 0.105 0.125 0.135 0.164 0.187 0.194 0.200 to 0.375
0.199 0.201 0.204 0.209 0.209 0.213 0.213 0.221 0.228
8 7 6 4 4 3 3 2 1
Note: for material thicknesses not given, use the next smaller thickness.
I-60
J.5.4 Minimum Edge Distance of Screws The distance from the center of a screw to an edge of a part shall not be less than 1.5 times the nominal diameter of the screw. See Section J.5.6.1 for the effect of edge distance on the bearing strength.
J.5.5 Screwed Connection Tension Screws in holes or screw slots and subjected to tension shall be designed for the limit states of pull-out, pull-over, and screw tensile rupture. The design tension strength fRn and the allowable tension strength Rn/W shall be determined as follows: f = 0.50 (LRFD) W = 3.0 (ASD building-type structures) W = 3.5 (ASD bridge-type structures) The nominal strength Rn for the limit state of pull-out shall be determined in accordance with Section J.5.5.1. The nominal strength Rn for the limit state of pull-over shall be determined in accordance with Section J.5.5.2. The nominal strength Rn for the limit state of screw tensile rupture shall be determined in accordance with Section J.5.5.3. For screws subjected to tension, the head of the screw or washer, if a washer is provided, shall have a nominal diameter not less than 5⁄16 in. (8 mm). Washers shall have a nominal thickness not less than 0.050 in. (1.3 mm). J.5.5.1 Pull-Out J.5.5.1.1 Screws in Holes
The nominal strength Rn for the limit state of pull-out of a screw in a hole is: a) For UNC threads (screw types C, D, F, G, and T) 1) for 0.060 in. ≤ Le ≤ 0.125 in. (1.5 mm ≤ Le ≤ 3 mm) Rn = KsDLeFty2
(J.5-1)
where Ks = 1.01 for 0.060 in. ≤ Le < 0.080 in. (1.5 mm ≤ Le < 2 mm) Ks = 1.20 for 0.080 in. ≤ Le ≤ 0.125 in. (2 mm ≤ Le ≤ 3 mm) Fty2 = tensile yield strength of member not in contact with the screw head D = nominal diameter of the screw 2) for 0.125 in. < Le < 0.25 in. (3 mm < Le < 6.3 mm) Rn = 1.2DFty2(0.25 - Le) + 1.16AsnFtu2(Le - 0.125) (J.5-2) January 2010
Table J.5.2 HOLE DIAMETERS FOR TYPE C, D, F, AND T SCREWS Metal Thickness (in.) screw size
0.050
0.060
0.083
0.109
0.125
0.140
⁄16
¼
0.1470 0.1660 0.1719 0.1910 0.2210 0.2280
0.1495 0.1719 0.1770 0.1990 0.2280 0.2344
3
5
⁄16
⁄8
½
0.1730 0.1770 0.1990 0.2280 0.2344
0.1990 0.2280 0.2344
3
Hole Diameter (in.) 8–32 10–24 10–32 12–24 ¼–20 ¼–28
0.1360 0.1495 0.1610
0.1360 0.1520 0.1610 0.1770
0.1360 0.1540 0.1610 0.1800 0.2055 0.2188
0.1405 0.1570 0.1660 0.1820 0.2090 0.2210
0.1405 0.1590 0.1660 0.1850 0.2130 0.2210
0.1440 0.1610 0.1660 0.1875 0.2130 0.2210
0.1495 0.1730 0.1770 0.1990 0.2280 0.2344
Note: for material thicknesses not given, use the next smaller thickness.
where Asn = thread stripping area of internal thread per unit length of engagement Ftu2 = tensile ultimate strength of member not in contact with the screw head 3) for 0.25 in. ≤ Le ≤ 0.375 in. (6.3 mm ≤ Le ≤ 10 mm) Rn = 0.58AsnLeFtu2
(J.5-3)
b) For spaced threads (screw types AB, B, BP, BF, and BT) 1) for 0.038 in. ≤ Le ≤ 2/n (1 mm < Le < 2/n) Rn = KsDLeFty2
(J.5-4)
where Ks = 1.01 for 0.038 in. ≤ Le < 0.080 in. (1 mm ≤ Le < 2 mm) Ks = 1.20 for 0.080 in. ≤ Le < 2/n (2 mm ≤ Le < 2/n) 2) for 2/n < Le < 4/n Rn = 1.2DFty2(4/n - Le) + 3.26DFtu2 (Le - 2/n) (J.5-5) 3) for 4/n ≤ Le ≤ 0.375 in. (4/n ≤ Le ≤ 8 mm) Rn = 1.63DLeFtu2
(J.5-6)
Figure J.5.1
J.5.5.1.2 Screws in Screw Slots
The nominal strength Rn for the limit state of pull-out of a screw in a screw slot with the dimensions shown in Figure J.5.1 and Table J.5.3 is: Rn = 0.29DLeFtu
(J.5-7)
where D = nominal diameter of the screw Ftu = tensile ultimate strength of the extrusion The screw embedment length in the screw slot Le shall not be less than 2D. January 2010
Table J.5.3 SCREW SLOT DIMENSIONS Screw Size
Screw Diameter D (in.)
Dss (in.) +/- 0.007 in.
8
0.164
0.147
10
0.190
0.169
12
0.216
0.190
¼
0.250
0.228
I-61
J.5.5.2 Pull-Over a) The nominal strength Rn for the limit state of pull-over for non-countersunk screws is: Rn = Cpovt1Ftu1(Dws - Dh)
(J.5-8)
for 0.06 in. ≤ t1 < 0.19 in. (1.5 mm ≤ t1 < 5 mm) and t1 /D ≤ 1.1. If t1 /D > 1.1, use t1 /D = 1.1 where Fty1 = tensile yield strength of the part in contact with the screw head
where pov = 1.0 for valley fastening and 0.7 for crown fastening C t1 = nominal thickness of the part in contact with the screw head or washer Ftu1 = tensile ultimate strength of the part in contact with the screw head or washer Dws = larger of the nominal washer diameter and the screw head diameter, but no greater than 5⁄8 in. (16 mm). (See Section J.5.5 for the washer thickness requirement.) Dh = nominal diameter of the hole in the material under the screw head The nominal pull-over strength for non-countersunk screws need not be less than the nominal pull-over strength computed from Equation J.5-10 for countersunk screws. Alternately, for parts with: 1) a nominal thickness of at least 0.040 in., 2) holes with the nominal diameters given in Table J.5.4, and 3) t1/Dws ≤ 0.5, the nominal strength Rn for the limit state of pull-over for non-countersunk screws with all-metal washers is: Rn = (1.0 + 1.7t1/Dws)Dws t1 Fty1
(J.5-9)
where t1 = nominal thickness of the part in contact with the screw head Fty1 = tensile yield strength of the part in contact with the screw head Dws = nominal diameter of the washer. The washer may be integral with the screw head.
Table J.5.4 HOLE SIZES FOR EQUATION J.5-9 Screw Diameter (in.)
Hole Diameter (in.)
Drill Size
8
0.164
0.177
16
10
0.190
0.201
7
12
0.216
0.228
1
¼
0.250
0.266
H
Screw Size
b) The nominal strength Rn for the limit state of pull-over for countersunk screws with an 82° nominal angle head is: Rn = (0.27 + 1.45t1/D)Dt1Fty1
I-62
(J.5-10)
J.5.5.3 Screw Tension For aluminum screws, the nominal strength Rn of a screw for the limit state of tensile rupture is: Rn = Ar Ftu /1.25
(J.5-11)
where Ar = root area of the screw Ftu = tensile ultimate strength of the screw = 68 ksi for 7075-T73 screws, = 62 ksi for 2024-T4 screws
J.5.6 Screwed Connection Shear Screws in holes and subjected to shear shall be designed for the limit states of bearing, tilting, and screw shear rupture. The design shear strength fRn and the allowable shear strength Rn/W shall be determined as follows: f = 0.50 (LRFD) W = 3.0 (ASD building-type structures) W = 3.5 (ASD bridge-type structures) The nominal strength Rn for the limit state of bearing shall be determined in accordance with Section J.5.6.1. The nominal strength Rn for the limit state of tilting shall be determined in accordance with Section J.5.6.2. The nominal strength Rn for the limit state of screw shear rupture shall be determined in accordance with Section J.5.6.3. J.5.6.1 Screw Bearing The nominal strength Rn for the limit state of bearing is Rn = detFtu ≤ 2DtFtu
(J.5-12)
where de = distance from the center of the screw to the edge of the part in the direction of force. t = for plain holes, nominal thickness of the connected part; for countersunk holes, nominal thickness of the connected part less ½ the countersink depth. Ftu = tensile ultimate strength of the connected part D = nominal diameter of the screw
January 2010
J.5.6.2 Screw Tilting For t2 ≤ t1, the nominal strength Rn for the limit state of tilting is: Rn = 4.2(t23D)1/2Ftu2
(J.5-13)
For t2 > t1, tilting is not a limit state.
For aluminum screws, the nominal strength Rn for the limit state of screw shear rupture is: (J.5-14)
where Ar = root area of the screw Fsu = shear ultimate strength of the screw = 41 ksi for 7075-T73 screws, = 37 ksi for 2024-T4 screws
J.6 Affected Elements of Members and Connectors This section applies to elements of members at connections and connectors such as plates, gussets, angles, and brackets.
J.6.1 Strength of Connectors in Tension The design strength fRn and the allowable strength Rn/W of connectors in tension shall be determined in accordance with Chapter D.
J.6.2 Strength of Connectors in Shear The design strength fRn and the allowable strength Rn/W of connectors in shear shall be the lesser value for the limit states of shear yielding and shear rupture. a) For shear yielding of connectors: Rn = Fsy Ag f = 1.00 (LRFD) W = 1.50 (ASD building-type structures) W = 1.68 (ASD bridge-type structures) b) For shear rupture of connectors: Rn = Fsu Anv f = 0.75 (LRFD) W = 1.95 (ASD building-type structures) W = 2.20 (ASD bridge-type structures)
J.6.3 Block Shear Strength The design strength fRn and the allowable strength Rn/W shall be determined for the limit state of block shear rupture as follows:
January 2010
a) For bolted connections on a failure path with shear on some segments and tension on the other segments: For Ftu Ant ≥ Fsu Anv
J.5.6.3 Screw Shear
Rn = Ar Fsu /1.25
f = 0.75 (LRFD) W = 1.95 (ASD building-type structures) W = 2.20 (ASD bridge-type structures)
Rn = Fsy Agv + Ftu Ant
(J.6-1)
otherwise Rn = Fsu Anv + Fty Agt
(J.6-2)
b) For welded connections on a failure path with shear on some segments and tension on the other segments: For FtuAgt ≥ FsuAgv Rn = Fsy Agv + Ftu Agt
(J.6-3)
otherwise Rn = Fsu Agv + Fty Agt
(J.6-4)
where Agv = gross area in shear Agt = gross area in tension Anv = net area in shear Ant = net area in tension
J.6.4 Strength of Connectors in Compression The design strength fRn and the allowable strength Rn /W of connectors in compression shall be determined in accordance with Chapter E.
J.7 Bearing Strength of Flat Surfaces and Pins The design bearing strength fRn and the allowable bearing strength Rn /W of surfaces in contact shall be determined as follows: f = 0.75 (LRFD) W = 1.95 (ASD building-type structures) W = 2.20 (ASD bridge-type structures) a) For pins in holes Rn = detFtu/1.5 ≤ 1.33DtFtu
(J.7-1)
I-63
J.8.2 Bearing Stiffeners
where D = nominal diameter of the pin t = thickness of the connected part de = distance from the center of a pin to the edge of a part, which shall not be less than 1.5D b) For flat surfaces Rn = 1.33Ftu Apb
(J.7-2)
where Apb = projected bearing area
J.8.3 Combined Crippling and Bending of Flat Webs
J.8 Flanges and Webs with Concentrated Forces J.8.1 Crippling of Flat Webs The design strength fRn and the allowable strength Rn/W for the limit state of web crippling shall be determined as follows: f = 0.75 (LRFD) W = 1.95 (ASD building-type structures) W = 2.20 (ASD bridge-type structures)
(J.8-1)
For concentrated forces applied at a distance from the member end that is less than d/2: wa(N + Cw2) R = 1.2C _____________ n Cwb
Combinations of bending and concentrated forces applied at a distance of one-half or more of the member depth from the member end shall be limited by the following formula:
( ) ( ) P 1.5 __ M __ + _ Pc Mc
1.5
≤ 1.0
(J.8-5)
where
For concentrated forces applied at a distance from the member end that equals or exceeds d/2: wa(N + Cw1) R = C __________ n Cwb
Bearing stiffeners at concentrated forces shall be sufficiently connected to the web to transmit the concentrated force. Such stiffeners shall form a tight and uniform bearing against the flanges unless welds designed to transmit the full concentrated force are provided between flange and stiffener. Only the part of a stiffener cross section outside the flangeto-web fillet shall be considered effective in bearing. The bearing stiffener shall meet the requirements of Chapter E with the length of the stiffener equal to the height of the web.
(J.8-2)
P = concentrated force M = bending moment in the member at the location of the concentrated force For LRFD Pc = design concentrated force determined in accordance with Section J.8.1 Mc = design flexural strength determined in accordance with Chapter F For ASD Pc = allowable concentrated force determined in accordance with Section J.8.1 Mc = allowable flexural strength determined in accordance with Chapter F
J.9 Roofing and Siding Connections
where:
J.9.1 Endlaps
____ Cwa = t2 sinθ (0.46Fcy + 0.02√EFcy )
(J.8-3)
Minimum endlaps shall be those given in Table J.9.1.
Cwb = Cw3 + Ri (1 - cosθ)
(J.8-4)
Table J.9.1 MINIMUM ENDLAPS
w1 = 5.4 in. (140 mm) C Cw2 = 1.3 in. (33 mm) Cw3 = 0.4 in. (10 mm) d = member depth N = length of the bearing at the concentrated force Ri: for shapes made by bending, Ri = inside bend radius at the juncture of the flange and web; for extruded shapes, Ri = 0 t = web thickness q = angle between the plane of web and the plane of the bearing surface (q ≤ 90°) I-64
Roofing slope > 2 on 12, < 3 on 12
Roofing slope ≥ 3 on 12
Siding
—
6 in. (150 mm)
4 in. (100 mm)
1 in. (25 mm) < d < 2 in. (50 mm)
9 in. (230 mm)
6 in. (150 mm)
4 in. (100 mm)
d ≥ 2 in. (50 mm)
9 in. (230 mm)
6 in. (150 mm)
6 in. (150 mm)
Depth of section d d ≤ 1 in. (25 mm)
January 2010
J.9.2 Sidelaps For sinusoidal corrugated sheet, the minimum sidelap width for roofing shall equal the pitch of the corrugations, and the minimum sidelap width for siding shall equal half the pitch. For trapezoidal sheet with a depth greater than 1 in. (25 mm) the minimum sidelap for both roofing and siding shall have a developed width equal to the width of the narrowest flat plus 2 in. (50 mm). Trapezoidal sheet with a
January 2010
depth of 1 in. (25 mm) or less shall have a sidelap of proven design with an anti-siphoning feature.
J.9.3 Fasteners in Laps The minimum size of fasteners used in end laps and side laps shall be #12 (5.5 mm) for screws and 3⁄16 in. (5 mm) diameter for rivets. The maximum spacing for sidelap fasteners shall be 12 in. (300 mm). Endlap fasteners shall be no more than 2 in. (50 mm) from the end of the overlapping sheet.
I-65
Chapter L Design for Serviceability L.1 General Provisions Serviceability is the preservation of a structure’s function under service load combinations.
Fe = element’s elastic local buckling stress determined using Section B.5.6 fa = maximum compressive stress in the element from service load combinations
If camber is required, its magnitude, direction, and location shall be shown on the structural drawings.
The effective width of elements subjected to flexure shall be placed next to the compression flange. Bending deflections shall be calculated using the compressive modulus of elasticity given in Table A.3.4 or Table A.3.4M.
L.3 Deflections
L.4 Vibration
Deflections caused by service load combinations shall not impair serviceability. For shapes with elements addressed by Sections B.5.4.1, B.5.4.2, B.5.4.3, B.5.5.1, or B.5.5.3 with fa > Fe, effective widths shall be used to determine the moment of inertia used to calculate deflections. The effective width be of such elements in compression is:
Vibration caused by service load combinations shall not impair serviceability.
L.2 Camber
L.5 Wind-Induced Motion Wind-induced motion caused by service load combinations shall not impair serviceability.
If fa ≤ Fe, be = b
(L.3-1)
L.6 Expansion and Contraction
____ If fa > Fe, be = b √ Fe /fa
(L.3-2)
Thermal expansion and contraction shall not impair serviceability.
where be = element’s effective width b = element’s width
I-66
L.7 Connection Slip Connection slip under service load combinations shall be precluded if it would impair serviceability.
January 2010
Chapter M Fabrication and Erection M.1 Layout M.1.1 Punch and Scribe Marks
shall not be drifted in a manner that distorts the metal. All chips and foreign matter between contacting surfaces shall be removed before assembly.
Punched or scribed layout marks shall not remain on fabricated material designed for fatigue.
M.5 Bending
M.1.2 Temperature Correction A temperature correction shall be applied where necessary in the layout of dimensions. The coefficient of thermal expansion used shall be per Section A.3.1.
M.2 Cutting M.2.1 Methods Cutting shall be by shearing, sawing, nibbling, routing, arc cutting, laser, or abrasive water jet. Edges which have been arc or laser cut shall be planed to remove edge cracks. Oxygen cutting is prohibited.
M.2.2 Edge Quality Cut edges shall be true, smooth, and free from excessive burrs or ragged breaks.
M.2.3 Re-entrant Corners Re-entrant corners shall be filleted.
M.3 Heating Alloys 535.0, 5083, 5086, 5154, and 5456 shall not be held at temperatures from 150°F (66°C) to 450°F (230°C). To hot form such alloys, they shall be 1) rapidly heated to a temperature not to exceed 550°F (290°C), 2) formed before the metal cools below 450°F (230°C), 3) rapidly cooled from 450°F to 150°F, and 4) designed using O temper strength. For other alloys heated above 200°F (93°C) during fabrication other than welding, time at temperature shall be limited as specified in Section A.3.1.1.
M.4 Holes M.4.1 Fabrication Methods Holes shall be punched or drilled. Holes shall be free from excessive burrs or ragged edges. Punching shall not be used for castings or if the metal thickness is greater than the diameter of the hole. The amount by which the diameter of a sub-punched hole is less than that of the finished hole shall be at least ¼ the thickness of the piece but not less than 1⁄ in. (0.8 mm). 32
Bend radii shall be large enough to avoid cracking.
M.6 Finishes M.6.1 Where Protective Coating Is Required Aluminum shall be provided with a protective coating when: a) alloy 2014 is in the presence of moisture, b) aluminum would otherwise be in contact with or fastened to dissimilar materials as described in Section M.7, c) aluminum is exposed to corrosive conditions.
M.6.2 Surface Preparation Surfaces to be painted shall be prepared immediately before painting by: a) chemical cleaning (such as a solution of phosphoric acid and organic solvents), or b) abrasion blasting, or c) unsealed anodizing, or d) chemical conversion coating, or e) using a procedure specified by the coating supplier.
M.6.3 Abrasion Blasting Abrasion blasting shall not be used if it distorts, perforates, or significantly reduces the thickness of the material blasted.
M.7 Contact with Dissimilar Materials Where aluminum is in contact with or fastened to the materials specified in Sections M.7.1 through M.7.3, direct contact between the aluminum and the other material shall be prevented as specified in those sections or by placing a compatible, nonporous isolator between the aluminum and the other material.
M.7.1 Steel Steel surfaces to be placed in contact with uncoated aluminum shall be painted with a coating suitable for the service. Where very corrosive conditions are expected, additional protection can be obtained by applying a sealant that excludes moisture from the joint during service. Aluminized or galvanized steel in contact with aluminum need not be painted. Stainless steel (300 series) in contact with aluminum need not be painted except in high chloride environments.
M.4.2 Hole Alignment
M.7.2 Wood, Fiberboard, or Other Porous Materials
If holes must be enlarged to admit fasteners, they shall be reamed. Poor matching holes shall be rejected. Holes
Aluminum surfaces to be placed in contact with wood, fiberboard, or other porous material that absorbs water shall
January 2010
I-67
be factory painted or given a heavy coat of alkali-resistant bituminous paint or other coating providing the equivalent protection before installation.
M.7.3 Concrete or Masonry Aluminum shall not be embedded in concrete with corrosive additives such as chlorides if the aluminum is electrically connected to steel. Unless the concrete or masonry remains dry after curing and no corrosive additives such as chlorides are used, aluminum surfaces to be placed next to or embedded in concrete or masonry shall be: a) given one coat of suitable paint, such as zinc molybdate primer conforming to Federal Specification TT-P-645B or equivalent, or b) given a heavy coating of alkali-resistant bituminous paint, or c) isolated with a suitable plastic tape or other isolation material.
M.7.4 Runoff from Heavy Metals Aluminum shall not be exposed to water that has come in contact with a heavy metal such as copper. The heavy metal shall be painted or coated, the drainage from the metal diverted away from the aluminum, or painted aluminum shall be used.
M.8 Fabrication Tolerances A fabricated member shall not vary from straight or from its intended curvature by more than its length divided by 960.
M.9 Welding Welding shall comply with the AWS D1.2 Structural Welding Code—Aluminum. Filler alloys shall be selected from Tables M.9.1 and M.9.2. The contract documents shall specify if visual inspection is required to be performed by AWS certified welding inspectors. When inspection other than visual inspection is required, the contract documents shall state the method,
I-68
extent, inspector qualifications, and acceptance criteria for such inspection.
M.10 Bolt Installation Unless the joint is a slip-critical connection, bolts need only be installed snug tight, the tightness that exists when all plies in a joint are in firm but not necessarily continuous contact. Slip-critical connections shall be tightened and inspected in accordance with the RCSC Specification for Structural Joints Using ASTM A325 or A490 Bolts.
M.11 Riveting M.11.1 Driven Head The driven head of aluminum rivets shall be flat or conepoint, with dimensions as follows: a) Flat heads shall have a diameter at least 1.4 times the nominal diameter of the rivet and a height at least 0.4 times the nominal diameter of the rivet. b) Cone-point heads shall have a diameter at least 1.4 times the nominal diameter of the rivet and a height to the apex of the cone at least 0.65 times the nominal diameter of the rivet. The nominal included angle at the apex of the cone shall be 127°.
M.11.2 Hole Filling Rivets shall fill holes completely. Rivet heads shall be concentric with the rivet holes and shall be in continuous contact with the surface of the part joined.
M.11.3 Defective Rivets Defective rivets shall be removed by drilling. The drill bit diameter shall not exceed the diameter of the replacement rivet.
M.12 Erection Tolerances Tolerances on erected dimensions shall be suitable for the intended service and consistent with the geometric imperfections used in the stability analysis conducted in accordance with Chapter C.
January 2010
January 2010
I-69
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
4043 (1100, 4047)
4043 (4047, 5183, 5356, 5556)
5086
5083, 5456
5052
5005, 5050
3004, Alclad 3004
4043 (1100, 4047)
2319 (4145)
DNW
DNW
DNW
DNW
DNW
DNW
DNW
4145
DNW
2219
5356 (5183, 5556)
5356 (4043, 4047, 5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183,5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (4043, 4047, 5183, 5556)
5356 (5183, 5556)
3004 Alclad 3004
5356 (4043, 4047, 5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5005, 5050
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5052
Notes: 1. This table is for structural applications subjected to normal atmospheric conditions using GTAW or GMAW. 2. DNW = Do Not Weld 3. Fillers in parentheses are acceptable alternates.
1060, 1100, 3003, Alclad 3003
4145
5356 (5183, 5556)
5154
2219
5356 (5183, 5556)
4043 (4047)
5356 (5183, 5556)
1060, 1100, 3003, Alclad 3003
5454
6005, 6005A, 6061, 6063, 6082, 6105, 6351, 6463
7005
Base Metal
Base Metal
5556 (5183)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5556 (5183)
5083, 5456
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5086
Table M.9.1 WELD FILLERS FOR WROUGHT ALLOYS
5654 (5183, 5356, 5556)
5654 (5183, 5356, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5154
5554 (5183, 5356, 5556)
5356 (5183, 5556)
5356 (5183, 5556)
5454
5356 (4043, 4047, 5183, 5556)
5356 (5183, 5556)
6005, 6005A, 6061, 6063, 6082, 6105, 6351, 6463
5556 (5183, 5356)
7005
Table M.9.2 WELD FILLERS FOR CAST ALLOYS Base Metal 535.0
356.0, A356.0, A357.0, 359.0
354.0, C355.0
1060, 1100, 3003, Alclad 3003
Base Metal
5356
4043 (4047)
4145
2219
DNW
4145
4145
3004, Alclad 3004
5356
4043 (4047)
4145 (4043, 4047)
5005, 5050
5356
4043 (4047)
4145 (4043, 4047)
5052
5356
4043 (4047)
4043 (4047)
5083, 5456
5356
5356
DNW
5086
5356
5356
DNW
5154
5356
4043
DNW
5454
5356
4043 (4047)
4043
6005, 6005A, 6061, 6063, 6082, 6105, 6351, 6463
5356
4043 (4047, 4145, 4643)
4145 (4043, 4047)
7005
5356
4043 (4047)
4145 (4043, 4047)
354.0, C355.0
DNW
4145
4145 (note 1)
356.0, A356.0, A357.0, 359.0
5356
4043 (note 1)
535.0
5356
Notes: 1. To weld C355.0 to itself, 4009 may be used; to weld A356.0 to itself, 4010 may be used; to weld A357.0 to itself, 4011 may be used. 2. DNW = Do Not Weld 3. Fillers in parentheses are acceptable alternates.
I-70
January 2010
Appendix 1 Testing 1.1 General Provisions Testing is an acceptable method for determining the nominal strengths of aluminum members, assemblies, or connections whose nominal strengths cannot be determined in accordance with Chapters A through L. Tests shall be conducted by a testing laboratory accredited by a nationally recognized accreditation service. General provisions for testing are given in Sections 1.2 and 1.3. Specific provisions for roofing and siding are given in Section 1.4.
1.2 Test Loading and Deflections Test loading and supports shall be representative of conditions during service. In tests that require measurement of deflection, a preload that is 20% of the design load shall be applied to set the specimen before testing. During testing, deflections shall be measured at the supports as well as at the point of maximum deflection, and the difference shall be taken as the specimen deflection. As an alternative, the structural performance of exterior aluminum fenestration products such as windows, curtain walls, and doors shall be determined in accordance with ASTM E 330.
1.3 Number of Tests and the Evaluation of Test Results
n 18 19 20 21 22 23 24 25 30 35 40 45 50 100
K 3.370 3.331 3.295 3.262 3.233 3.206 3.181 3.158 3.064 2.994 2.941 2.897 2.863 2.684
1.3.2 Tests for Determining Structural Performance For members and assemblies, no fewer than four identical specimens shall be tested. If any individual result deviates from the average result by more than 10%, at least three more tests shall be performed. For LRFD, the design strength shall be the average of all test results multiplied by the resistance factor f determined as follows: o
2 M
+ VF2 + CnV P2 + VQ2
(1.3-2)
For ASD, the allowable strength shall be the average of all test results divided by the safety factor W determined as follows:
In determining yield strength and ultimate strength of material or fasteners, sufficient tests shall be conducted to statistically establish the strength which 99% of the material is expected to exceed with a confidence of 95%. This strength shall be calculated as follows: (1.3-1)
where Xa = strength which 99% of the material is expected to exceed with a confidence of 95% Xm = mean of the test results Sx = standard deviation of the test results K = statistical coefficient based on the number of tests n. K is a one-sided factor for 99% of the population exceeding Xa with a confidence of 95%. Values of K for the following values of n are:
January 2010
K 10.55 7.042 5.741 5.062 4.641 4.353 4.143 3.981 3.852 3.747 3.659 3.585 3.520 3.463 3.415
φ = 1.5MmFme-β √ V
1.3.1 Tests for Determining Mechanical Properties
Xa = Xm - KSx
n 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1.05α + 1 β √ V Ω = ___________ e MmFm (α + 1) o
2 M
+ VF2 + CnV P2 + VQ2
(1.3-3)
where a = Dn /Ln; in lieu of calculation by the above formula, a = 0.2 bo = the target reliability index = 2.5 for columns, beams and beam-columns, = 3.0 for tension members, and = 3.5 for connections. n2 - 1 Cn = correction factor = ______ n2 - 3n Dn = nominal dead load e = base for natural logarithms ≈ 2.72 Fm = mean value of the fabrication factor Ln = nominal live load Mm = mean value of the material factor
I-71
n = number of tests Xi = failure load of ith test Xm = average value of failure loads in all tests n Xi ∑ i=1 = ____ n VF = coefficient of variation of the fabrication factor VM = coefficient of variation of the material factor VP = coefficient of variation of the ratio of the observed failure loads divided by the average value of all the observed failure loads n Xi 2 n ∑ 2 Xi X - i=1 m X n ∑ m = i=1 n-1 VQ = coefficient of variation of the loads = √(0.105Dn)2 + (0.25Ln)2 ; in lieu of calculation by 1.05Dn + Ln the above formula, VQ = 0.21
√
( ) ( )
The following values shall be used when documented statistical data established from a sufficient number of results on material properties does not exist for the member or connection: m = 1.10 for behavior governed by the yield stress M = 1.00 for behavior governed by the ultimate stress Fm = 1.00 VM = 0.06 VF = 0.05 for structural members and bolted connections = 0.15 for welded connections In evaluating test results, adjustment shall be made for any differences between the yield strength of the material from which the tested sections are formed and the yield strength specified for the material which the manufacturer intends to use. If the tensile yield strength of the aluminum from which the tested sections are formed is greater than the specified value, the test results shall be adjusted down to the specified yield strength of the aluminum which the manufacturer intends to use. The test results shall not be adjusted upward if the yield strength of the test specimen is less than the specified yield strength. Similar adjustments shall be made on the basis of tensile ultimate strength instead of yield strength when behavior is governed by the tensile ultimate strength. Adjustments shall also be made for differences between nominal section properties and those of tested sections.
1.4 Testing Roofing and Siding The bending strength of roofing and siding shall be established from tests when any of the following conditions apply. a) Web angles are asymmetrical about the centerline of a valley, rib, flute, crimp, or other corrugation; b) Web angles are less than 45°; I-72
c) Aluminum panels are alternated with panels composed of any material having significantly different strengths or deflection characteristics; d) Flats spanning from rib to rib or other corrugation in the transverse direction have a width to thickness ratio greater than either of the following: (1) 1230 where q is the design load in psf 3– √q 447 where q is the design load in kN/m2 3– √q F (2) 435 ty where Fty is in ksi and q is in psf q Fty 37 where Fty is in MPa and q is in kN/m2 ; q e) Panel ribs, valleys, crimps, or other corrugations are of unequal depths; f) Specifications prescribe less than one fastener per rib to resist negative or uplift loading at each purlin, girt, or other transverse supporting member; or g) Panels are attached to supporting members by profile interlocking straps or clips.
)
(
√ ( √
)
1.4.1 Test Method Tests shall be conducted in accordance with ASTM E 1592.
1.4.2 Different Thicknesses Only the thinnest and thickest specimens manufactured are required to be tested when panels are of like configuration, differing only in material thickness. Where the failure of the test specimens is from bending stress, the bending strength for intermediate thicknesses shall be interpolated as follows:
(
)
log Mi = log M1 + log ti - log tmin (log M2 - log M1) log tmax - log tmin (1.4-1) where Mi = bending strength of member of intermediate thickness ti M1 = bending strength of member of thinnest material M2 = bending strength of member of thickest material ti = thickness of intermediate thickness material tmin = thickness of thinnest material tested tmax = thickness of thickest material tested
1.4.3 Design and Allowable Strengths Design strengths shall be determined using the resistance factors given in Chapter F for bending and Chapter J applied to the minimum test strength achieved for fasteners. Allowable strengths shall be determined using the safety factors given in Chapter F for bending and Chapter J applied to the minimum test strength achieved for fasteners.
1.4.4 Deflections Live load deflections shall meet the requirements of Section L.3. January 2010
Appendix 3 Design for Fatigue 3.1 General Provisions Welded details, mechanically fastened joints, and wrought material subjected to fatigue shall meet all the static requirements of this Specification as well as the requirements of this Appendix. Fatigue design of castings shall be made by testing in accordance with Appendix 1. Categories of details for fatigue design parameters shall be chosen from Figure 3.1 and Table 3.1. The maximum and minimum stresses used to calculate the stress range are nominal stresses perpendicular to the expected plane of cracking determined by elastic methods.
fatigue consideration shall be needed. The allowable stress range Srd shall not be less than the value from Equation 3.2-2 when N = 5 × 106 cycles and shall not be greater than the value from Equation 3.2-2 when N = 105 cycles.
3.3 Variable Amplitude Loading For variable amplitude loading: Sre ≤ Srd where Sre = equivalent stress range
3.2 Constant Amplitude Loading
(
(3.2-1)
where Sra = applied stress range, the algebraic difference between the minimum and maximum calculated stress Srd = allowable stress range Srd = Cf N -1/m (3.2-2) Cf , m = constants from Table 3.2 N = number of cycles to failure If the applied stress range Sra is less than the constant amplitude fatigue limit given in Table 3.2, no further
January 2010
Ns
)
Sre = ∑αi S mri
For constant amplitude loading Sra ≤ Srd
(3.3-1)
i=1
1/m
(3.3-2)
Srd = allowable stress range Srd = Cf N -1/m (3.3-3) ai = number of cycles in the spectrum of the ith stress range divided by the total number of cycles Sri = ith stress range in the spectrum Cf , m = constants from Table 3.2 NS = number of stress ranges in the spectrum N = number of cycles to failure
The allowable stress range Srd shall not exceed the value from Equation 3.3-3 when N = 105 cycles. If the maximum stress range in the spectrum is less than the constant amplitude fatigue limit, no further fatigue assessment is needed.
I-73
Figure 3.1 FATIGUE DESIGN DETAILS
I-74
January 2010
Figure 3.1 FATIGUE DESIGN DETAILS (Continued)
January 2010
I-75
weld top side first
≥ 23
Figure 3.1 FATIGUE DESIGN DETAILS (Continued)
I-76
January 2010
Table 3.1 STRESS CATEGORY General Condition
Detail
Detail Fatigue Design Category Details (note 1)
Plain Material
Base metal with rolled, extruded, drawn, or cold finished surfaces; cut or sheared surfaces with ANSI/ASME B46.1 surface roughness ≤ 1000 µin. (25µmm)
A
1, 2
Built-up Members
Base metal and weld metal in members without attachments and built up of plates or shapes connected by continuous full or partial penetration groove welds or continuous fillet welds parallel to the direction of applied stress. Flexural stress in base metal at the toe of welds on girder webs or flanges adjacent to welded transverse stiffeners. Base metal at the end of partial-length welded cover plates with square or tapered ends, with or without welds across the ends.
B
3, 4, 5
C
6, 21
E
5
B D E E
7 7 7 8
Base metal at intermittent fillet welds Base metal at the junction of axially loaded members with fillet-welded end connections. Welds shall be disposed about the axis of the members so as to balance weld stresses. Shear stress in weld metal of continuous or intermittent longitudinal or transverse fillet welds
E E
15, 17
F
5, 15, 18
Base metal and weld metal at full-penetration groove welded splices of parts of similar cross section ground flush, with grinding in the direction of applied stress and with weld soundness established by radiographic or ultrasonic inspection. Base metal and weld metal at full-penetration groove welded splices at transitions in width or thickness, with welds ground to slopes ≤ 1: 2.5, with grinding in the direction of applied stress, and with weld soundness established by radiographic or ultrasonic inspection. Base metal and weld metal at full-penetration groove welded splices with or without transitions with slopes ≤ 1: 2.5, when reinforcement is not removed and/or weld soundness is not established by radiographic or ultrasonic inspection. Base metal and weld metal at full-penetration groove welds with permanent backing.
B
9, 10
B
11, 12
C
9, 10, 11, 12
E
22
B C D C
13 13 13 19
D E
14 14, 19, 20
B C D
16 16 16
F1
23
Mechanically Base metal at the gross section of slip-critical connections and at the net section of bearing conFastened nections, where the joint configuration does not result in out-of-plane bending in the connected Connections material and the stress ratio (the ratio of minimum stress to maximum stress) RS is (note 2) RS ≤ 0 0 < RS < 0.5 0.5 ≤ RS Base metal at the gross section of slip-critical connections and at the net section of bearing connections, where the joint configuration results in out-of-plane bending in connected material. Fillet Welds
Groove Welds
Attachments
Luminaire Base Welds
Base metal detail of any length attached by groove welds subject to transverse and/or longitudinal loading, with a transition radius R ≥ 2 in. (50 mm) and with the weld termination ground smooth: R ≥ 24 in. (610 mm) 24 in. > R ≥ 6 in. (150 mm) 6 in. > R ≥ 2 in. (50 mm) Base metal at a detail attached by groove welds or fillet welds with a detail dimension parallel to the direction of stress a < 2 in. (50 mm) Base metal at a detail attached by groove welds or fillet welds subject to longitudinal loading, with a transition radius, if any, < 2 in. (50 mm): 2 in. (50 mm) ≤ a ≤ 12b or 4 in. (100 mm) a > 12b or 4 in. (100 mm) Base metal at a detail of any length attached by fillet welds or partial-penetration groove welds in the direction parallel to the stress, with a transition radius R ≥ 2 in. (50 mm), and the weld termination is ground smooth: R ≥ 24 in. (610 mm) 24 in. > R ≥ 6 in. (150 mm) 6 in. > R ≥ 2 in. (50 mm) Base metal and filler metal at a pair of circumferential fillet welds at least 0.48D apart in a tube’s longitudinal direction, where D = the outside diameter of the tube. Fillet welds shall be sufficient to develop the static bending strength of the tube and be placed in the following order: weld the top of the base and the tube, then weld the end of the tube and the bottom of the base. The base shall be for a top mounted luminaire or as a support for a short arm, defined as that producing no more than 5 ksi (35 MPa) tensile dead load stress in the tube at top of the base.
Notes: 1. See Figure 3.1. These examples are provided as guidelines and are not intended to exclude other similar details. 2. Tensile stresses are considered to be positive and compressive stresses are considered to be negative.
January 2010
I-77
Table 3.2 CONSTANTS FOR S-N CURVES Constant Amplitude Fatigue Limit
Cf Detail Category
ksi
MPa
m
ksi
MPa
A
96.5
665
6.85
10.2
70
B
130
900
4.84
5.4
37
C
278
1920
3.64
4.0
28
D
157
1080
3.73
2.5
17
E
160
1100
3.45
1.8
13
F
174
1200
3.42
1.9
13
200
7.31
3.2
22
F1
29.0
Notes: 1. Constant amplitude fatigue limit is based on N = 5 × 106 except for detail category F1 where N = 10 × 106.
I-78
January 2010
Appendix 4 Design for Fire Conditions This appendix addresses the design and evaluation of aluminum structures exposed to fire. It includes criteria for determining heat input, thermal expansion, and reduction in mechanical properties of aluminum at elevated temperatures.
4.1 General Provisions Design for fire conditions shall comply with the requirements for design by engineering analysis given in Section 4.2 or the requirements for design by qualification testing given in Section 4.3. The analysis methods in Section 4.2 document the anticipated performance of aluminum structures when subjected to design-basis fires, and provide evidence of compliance with the performance objectives of Section 4.1.2. The qualification testing methods in Section 4.3 document the fire resistance of aluminum structures subject to the standardized fire testing protocols required by building codes.
4.1.1 Definitions This appendix uses the following terms as defined below: active fire protection: structural materials and systems activated by a fire to mitigate adverse effects or notify people to take action to mitigate adverse effects. compartmentation: the enclosure of a structure’s space with elements that have a specific fire endurance. design-basis fire: a set of conditions that define the development of a fire and the spread of combustion products in a structure. elevated temperatures: temperatures in excess of the anticipated ambient temperature, experienced by structural elements as a result of fire. fire: destructive burning, as manifested by any or all of the following: light, flame, heat, or smoke. fire barrier: an element of construction formed of fire-resisting materials and tested in accordance with ASTM E 119 or other approved standard fireresistance test to demonstrate compliance with the building code. fire endurance: a measure of the elapsed time during which a material or assembly continues to exhibit fire resistance. fire resistance: the property of assemblies that prevents or retards the passage of excessive heat, hot gases, or flames under conditions of use and enables them to continue to perform a stipulated function. flashover: the transition to a state of total surface involvement in a fire of combustible materials within an enclosure. heat flux: radiant energy per unit surface area. heat release rate: the rate at which thermal energy is generated by a burning material. January 2010
restrained construction: floor and roof assemblies and individual beams in buildings where the surrounding or supporting structure is capable of resisting substantial thermal expansion throughout the range of anticipated elevated temperatures. unrestrained construction: floor and roof assemblies and individual beams in buildings that are assumed to be free to rotate and expand throughout the range of anticipated elevated temperatures.
4.1.2 Performance Objectives Structural components, members, and frame systems shall be designed to maintain their load-bearing function during the design-basis fire and to satisfy other performance requirements specified for the building occupancy. Deformation criteria shall be applied where the means of providing structural fire resistance or the design criteria for fire barriers requires consideration of the deformation of the load-carrying structure. Forces and deformations from the design-basis fire shall not cause a horizontal or vertical breach of the compartment of fire origin.
4.1.3 Load Combinations and Required Strength The required strength of the structure and its elements shall be determined using load and resistance factor design for the following gravity load combination: [0.9 or 1.2]Dn + T + 0.5Ln + 0.2Sn
(4-1)
where n = nominal dead load D Ln = nominal live load Sn = nominal snow load T = nominal forces and deformations due to the design-basis fire defined in Section 4.2.1. Dn, Ln, and Sn shall be the nominal loads specified in ASCE 7.
4.2 Design for Fire Conditions by Analysis 4.2.1 Design-Basis Fire A design-basis fire shall be defined that describes heating conditions for the structure. These heating conditions shall relate to the fuel commodities and compartment characteristics present in the assumed fire area. The fuel load density based on the occupancy of the space shall be considered when determining the total fuel load. Heating conditions shall be specified in terms of a heat flux or temperature of the upper gas layer created by the fire. The variation of the heating conditions with time shall be determined for the duration of the fire. I-79
When the analysis methods in Section 4.2 are used to demonstrate an equivalency as an alternative material or method as permitted by a building code, the design-basis fire shall be determined in accordance with ASTM E 119. 4.2.1.1 Localized Fire Where the heat release rate from the fire is insufficient to cause flashover, a localized fire exposure shall be assumed. In such cases, the fuel composition, arrangement of the fuel, and area occupied by the fuel shall be used to determine the radiant heat flux from the flame and smoke plume to the structure. 4.2.1.2 Post-Flashover Compartment Fires Where the heat release rate from the fire is sufficient to cause flashover, a post-flashover compartment fire shall be assumed. The determination of the temperature versus time profile resulting from the fire shall include fuel load, ventilation characteristics to the space (natural and mechanical), compartment dimensions, and thermal characteristics of the compartment boundary. 4.2.1.3 Exterior Fires The exposure of exterior structure to flames projecting from wall openings as a result of a post-flashover compartment fire shall be considered along with the radiation from the interior fire through the opening. The shape and length of the flame projection and distance between the flame and the exterior structure shall be used to determine the heat flux to the aluminum. The method in Section 4.2.1.2 shall be used to define the interior compartment fire characteristics. 4.2.1.4 Fire Duration The fire duration in a particular area shall be determined by considering the total combustible mass, the available fuel in the space. In the case of a localized fire or a postflashover fire, the time duration shall be determined as the total combustible mass divided by the mass loss rate, except where determined from Section 4.2.1.2.
4.2.3 Material Properties at Elevated Temperatures 4.2.3.1 Mechanical Properties The deterioration in strength and stiffness of structural members shall be accounted for in the structural analysis. The modulus of elasticity at elevated temperatures Em shall be determined from test data or Table 4.1. Yield strengths Ftym and ultimate strengths Ftum at elevated temperatures shall be determined from test data or Table 4.2. 4.2.3.2 Thermal Expansion Thermal expansion for temperatures between 70°F and 600°F (20°C and 300°C) shall be determined using a coefficient of thermal expansion for aluminum of 14.2 × 10-6/°F (25.6 × 10-6/°C). 4.2.3.3 Specific Heat The specific heat of aluminum alloys is 0.23 Btu/lb/°F (960 J/kg/°C) at 212°F (100°C).
4.2.4 Structural Design Requirements 4.2.4.1 General Structural Integrity Structures shall provide adequate strength and deformation capacity to withstand the conditions developed during the design-basis fire within the prescribed limits of deformation. The structural system shall be designed to sustain local damage with the structural system as a whole remaining stable. Continuous load paths shall be provided to transfer all forces from the region exposed to fire to the final point of resistance. The foundation shall be designed to resist the forces and to accommodate the deformations developed during the design-basis fire.
Table 4.1 MODULUS OF ELASTICITY AT ELEVATED TEMPERATURES Aluminum Temperature (°F)
(°C)
Em/E 6xxx alloys
75
24
1.00
200
93
1.00
212
100
0.96
300
149
0.92
350
177
0.90
400
204
0.87
450
232
0.84
4.2.2 Temperatures in Structural Systems under Fire Conditions
500
260
0.80
600
316
0.69
Temperatures within structural members, components, and frames due to heating conditions posed by the designbasis fire shall be determined by a heat transfer analysis.
700
371
0.56
1000
538
0.00
4.2.1.5 Active Fire Protection Systems The effects of active fire protection systems shall be considered when defining the design-basis fire. Where automatic smoke and heat vents are installed in non-sprinklered spaces, the resulting smoke temperature shall be determined from calculation.
I-80
Interpolate for temperatures between those given in the table.
January 2010
Table 4.2 STRENGTHS AT ELEVATED TEMPERATURES Aluminum Temperature
6061-T6
6063-T5
6063-T6
(°F)
(°C)
Ftym/Fty
Ftum/Ftu
Ftym/Fty
Ftum/Ftu
Ftym/Fty
Ftum/Ftu
75
24
1.00
1.00
1.00
1.00
1.00
1.00
200
93
1.00
1.00
1.00
1.00
1.00
1.00
212
100
0.95
0.91
0.93
0.91
0.90
0.89
300
149
0.90
0.84
0.89
0.84
0.84
0.80
350
177
0.88
0.80
0.89
0.84
0.77
0.71
400
204
0.75
0.67
0.68
0.63
0.58
0.57
450
232
0.58
0.53
0.50
0.50
0.42
0.43
500
260
0.40
0.40
0.36
0.38
0.29
0.29
600
316
0.20
0.20
0.20
0.20
0.11
0.11
700
371
0.08
0.08
0.08
0.08
0.06
0.07
1000
538
0.00
0.00
0.00
0.00
0.00
0.00
Interpolate for temperatures between those given in the table.
4.2.4.2 Strength Requirements and Deformation Limits Conformance of the structural system to these requirements shall be demonstrated by constructing a mathematical model of the structure based on principles of structural mechanics and evaluating this model for the internal forces and deformations in the members of the structure developed by the temperatures of the design-basis fire. Individual members shall be provided with adequate strength to resist the shears, axial forces, and moments determined by this analysis. Connections shall develop the strength of the connected members or the forces indicated above. Where the means of providing the fire resistance requires the consideration of deformation criteria, the deformation of the structural system or members thereof under the design-basis fire shall not exceed the prescribed limits. 4.2.4.3 Methods of Analysis 4.2.4.3.1 Advanced Methods of Analysis
The methods of analysis in this section are permitted for the design of all aluminum structures for fire conditions. The design-basis fire exposure shall be that determined in Section 4.2.1. The analysis shall include both a thermal response and the mechanical response to the designbasis fire. The thermal response shall produce a temperature field in each structural element as a result of the design-basis fire and shall incorporate temperature-dependent thermal properties of the structural elements and fire-resistive materials in accordance with Section 4.2.2. The mechanical response results in forces and deformations in the structural system subjected to the thermal response calculated from the design-basis fire. The mechanical response shall explicitly account for the deterioraJanuary 2010
tion in strength and stiffness with increasing temperature, the effect of thermal expansion, and large deformations. Boundary conditions and connection fixity in the analysis shall be representative of the proposed structural design. Material properties shall be as given in Section 4.2.3. The resulting analysis shall consider all relevant limit states, such as excessive deflections, connection fractures, and overall and local buckling. 4.2.4.3.2 Simple Methods of Analysis
The methods of analysis in this section apply to evaluating the performance of individual members at elevated temperatures during exposure to fire. Support and restraint conditions (forces, moments, and boundary conditions) at normal temperatures may be assumed to remain unchanged throughout the fire exposure. 1) Tension members It is permitted to model the thermal response of a tension member using a one-dimensional heat transfer equation with heat input from the design-basis fire defined in Section 4.2.1. The design strength of a tension member shall be determined using the provisions of Chapter D with aluminum properties as given in Section 4.2.3 and assuming a uniform temperature over the cross section using the temperature equal to the maximum aluminum temperature. 2) Compression members It is permitted to model the thermal response of a compression member using a one-dimensional heat transfer equation with heat input from the design-basis fire defined in Section 4.2.1. The design strength of a compression member shall be determined using the provisions of Chapter E with aluminum properties as given in Section 4.2.3. I-81
3) Flexural members It is permitted to model the thermal response of a flexural member using a one-dimensional heat transfer equation to calculate bottom flange temperature and to assume that this bottom flange temperature is constant over the depth of the member. Heat input shall be determined from the design-basis fire defined in Section 4.2.1. The design strength of a flexural member shall be determined using the provisions of Chapter F with aluminum properties as given in Section 4.2.3. 4.2.4.4 Design Strength The design strength shall be determined in accordance with Section B.3. The nominal strength Rn shall be determined using the material properties given in
I-82
Section 4.2.3 at the temperature developed during the design-basis fire.
4.3 Design by Qualification Testing 4.3.1 Qualification Standards Structural members and components in aluminum structures shall be qualified for the rating period in conformance with ASTM E 119.
4.3.2 Restrained Construction A restrained condition exists when the surrounding or supporting structure is capable of resisting actions caused by thermal expansion throughout the range of anticipated elevated temperatures.
January 2010
Appendix 5 Evaluation of Existing Structures 5.1 General Provisions
5.3 Evaluation by Structural Analysis
These provisions apply to evaluating the strength or serviceability of existing members, connections, or structures. Evaluations shall be performed by structural analysis or both structural analysis and load testing.
5.3.1 Dimensions
5.2 Material Properties
5.3.2 Strength Evaluation
5.2.1 Wrought and Cast Products
Loads shall be determined in accordance with Section B.2 or the maximum load that can be withstood shall be determined. Load effects in the structure shall be detemined by structural analysis. The strength of members and connections shall be determined using the Specification for Aluminum Structures.
Unless the aluminum alloy and temper used in the structure are identified from records, specimens shall be cut from the structure and both: a) Chemical composition tests shall be conducted to determine the alloy, and b) Tensile tests shall be conducted in accordance with ASTM B 557 to determine the tensile yield strength, tensile ultimate strength, and elongation to determine the temper. Mechanical properties given in the appropriate ASTM material specification for the alloy, temper, and product that were determined to have been used in the structure shall be used in the structural analysis.
5.2.2 Welds Where structural performance depends on existing welds: a) The filler metals used in the structure shall be identified from records or chemical analysis of representative samples of weld metal. b) If welds do not meet the visual inspection criteria of AWS D1.2, additional inspection shall be conducted to determine their strength.
5.2.3 Bolts and Rivets Unless bolt or rivet strength can be determined from records or markings, representative samples shall be removed and tested to determine tensile strength in accordance with ASTM F 606 or ASTM F 606M.
January 2010
Dimensions and the condition of structural members and connections shall be determined from records and/or from a field survey.
5.3.3 Serviceability Evaluation Deformations shall be calculated at service loads.
5.4 Evaluation by Load Testing To prevent excessive permanent deformation or collapse during load testing, the structure shall be analyzed and a written testing plan prepared before testing. Test loads shall be applied incrementally in accordance with the written testing plan. Test loads shall not exceed a factored load of 1.0Dn + 1.4Ln. The structure shall be visually inspected for signs of distress or imminent failure at each load increment. Deformations shall be recorded at each load increment and one hour and 24 hours after the removal of the load.
5.5 Evaluation Report The evaluation shall be documented by a written report that includes: a) whether the evaluation was performed by structural analysis or a combination of structural analysis and load testing; b) when testing is performed, the loads and load combinations used and the load-deformation and time-deformation relationships observed; c) information obtained from records and material testing; d) the allowable strength or design strength of the structure; and e) the date the evaluation was performed.
I-83
Appendix 6 Design of Braces for Columns and Beams This appendix addresses strength and stiffness requirements for braces for columns and beams.
6.1 General Provisions
( )
2P bbr = Ω ___r Lb
(ASD)
(6-2)
where
The available strength and stiffness of bracing members and connections shall equal or exceed the required strength and stiffness, respectively, given in this appendix. Columns with end and intermediate braced points that meet the requirements of Section 6.2 shall be designed using an unbraced length L equal to the distance between the braced points with an effective length factor k = 1.0. Beams with intermediate braced points that meet the requirements of Section 6.3 shall be designed using an unbraced length Lb equal to the distance between the braced points. As an alternate to the requirements of Sections 6.2 and 6.3, a second-order analysis that includes initial out-ofstraightness of the member to be braced shall be used to obtain the brace strength and stiffness requirements. For all braces, f = 0.75 (LRFD), and W = 2.00 (ASD), except that for nodal torsional bracing of beams, W = 3.00.
Lb = distance between braces For LRFD, Pr = required axial compression strength using LRFD load combinations. For ASD, Pr = required axial compression strength using ASD load combinations.
6.2.2 Nodal Bracing For nodal braces equally spaced along the column: The required strength is Prb = 0.01Pr
(6-3)
6.1.1 Bracing Types
The required stiffness is
a) A relative brace controls movement of the braced point with respect to adjacent braced points. b) A nodal brace controls movement of the braced point without direct interaction with adjacent braced points. c) Continuous bracing is bracing attached along the entire member length.
8Pr b = _1_ ___ br φ Lb
(LRFD)
(6-4)
8P bbr = Ω ___r Lb
(ASD)
(6-4)
( ) ( )
where
6.1.2 Bracing Orientation The brace strength (force or moment) and stiffness (force per unit displacement or moment per unit rotation) requirements given in this appendix are perpendicular to the member braced. The available brace strength and stiffness perpendicular to the member braced for inclined braces shall be adjusted for the angle of inclination. The determination of brace stiffness shall include the effects of member properties and connections.
Lb = distance between braces. In Equation 6-4, Lb need not be taken less than the maximum unbraced length kL permitted for the column based on the required axial strength Pr. For LRFD, Pr = required axial compression strength using LRFD load combinations. For ASD, Pr = required axial compression strength using ASD load combinations.
6.2 Column Bracing 6.3 Beam Bracing
6.2.1 Relative Bracing The required strength is Prb = 0.004Pr
(6-1)
The required stiffness is
( )
2Pr b = _1_ ___ br φ Lb I-84
(LRFD)
(6-2)
Beams and trusses shall be restrained against rotation about their longitudinal axis at support points. Beam bracing shall prevent relative displacement of the top and bottom flanges (twist of the section). Lateral stability of beams shall be provided by lateral bracing, torsional bracing, or a combination of the two. Inflection points shall not be considered braced points unless they are provided with braces meeting the requirements of this appendix. January 2010
6.3.1 Lateral Bracing Lateral braces shall be attached at or near the compression flange, except: a) At the free end of cantilever members, lateral braces shall be attached at or near the tension flange. b) For beams subjected to double curvature bending, lateral bracing shall be attached to both flanges at the brace point nearest the inflection point. 6.3.1.1 Relative Bracing The required strength is Prb = 0.008MrCd /ho
For LRFD, Mr = required flexural strength using LRFD load combinations. For ASD, Mr = required flexural strength using ASD load combinations.
6.3.2 Torsional Bracing (6-5)
The required stiffness is
( ) ( )
Lb = distance between braces. In Equation 6-8, Lb need not be taken less than the maximum unbraced length permitted for the beam based on the required flexural strength Mr.
4MrCd b = _1_ ______ br φ Lbho
(LRFD)
(6-6)
4MrCd bbr = Ω ______ Lbho
(ASD)
(6-6)
where
Bracing shall be attached to the braced member at any cross section location on the member and need not be attached near the compression flange. 6.3.2.1 Nodal Bracing The required strength is 0.024MrL M = ________ rb nCbLb
(6-9)
The required stiffness of the brace is
ho = distance between flange centroids Cd = 1.0 except Cd = 2.0 for the brace closest to the inflection point in a beam subject to double curvature Lb = distance between braces For LRFD, Mr = required flexural strength using LRFD load combinations. For ASD, Mr = required flexural strength using ASD load combinations. 6.3.1.2 Nodal Bracing
(6-7)
The required stiffness is
( ) ( )
10MrCd b = _1_ _______ br φ Lbho
(LRFD)
(6-8)
10MrCd bbr = Ω _______ Lbho
(ASD)
(6-8)
where ho = distance between flange centroids Cd = 1.0 except Cd = 2.0 for the brace closest to the inflection point in a beam subject to double curvature January 2010
(
(6-10)
)
If bsec < bT, torsional beam bracing shall not be used.
( ) ( ) (
2.4LMr2 b = _1_ _______ T φ nEIyCb2
(LRFD)
(6-11)
2.4LM 2 bT = Ω _______r2 nEIyCb
(ASD)
(6-11)
)
(6-12)
3 3.3E 1.5h ts bs3 ot w b = ____ ______ + ___ sec ho 12 12
The required strength is Prb = 0.02MrCd /ho
bT b = ________ Tb bT 1 - ___ bsec
where L = span length. In Equation 6-9, Lb need not be taken less than the maximum unbraced length permitted for the beam based on the required flexural strength Mr. n = number of nodal braced points in the span Iy = out-of-plane moment of inertia Cb = beam coefficient determined in accordance with Section F.1.1 tw = beam web thickness ts = beam web stiffener thickness bs = stiffener width for one-sided stiffeners (use twice the individual width for pairs of stiffeners) bT = overall brace system stiffness I-85
bsec = web distortional stiffness, including the effect of web transverse stiffeners, if any For LRFD, Mr = required flexural strength using LRFD load combinations. For ASD, Mr = required flexural strength using ASD load combinations. Web stiffeners shall extend the full depth of the braced member and shall be attached to the flange if the torsional brace is also attached to the flange. Alternatively, the stiffener may end a distance of 4tw from any beam flange that is not directly attached to the torsional brace. 6.3.2.2 Continuous Bracing For continuous bracing, use Equations 6-9 and 6-10 with the following modifications: a) L/n = 1.0; b) Lb shall be taken as the maximum unbraced length permitted for the beam based on the required flexural strength Mr; c) The web distortional stiffness shall be taken as: b = 3.3Et ______3w sec 12ho
I-86
(6-13)
6.4 Beam-Column Bracing For beam-columns, the required strength and stiffness for axial force shall be determined as specified in Section 6.2, and the required strength and stiffness for flexure shall be determined as specified in Section 6.3. The values so determined shall be combined as follows: a) When relative lateral bracing is used, the required strength is the sum of the values determined using Equations 6-1 and 6-5, and the required stiffness is the sum of the values determined using Equations 6-2 and 6-6. b) When nodal lateral bracing is used, the required strength is the sum of the values determined using Equations 6-3 and 6-7, and the required stiffness is the sum of the values determined using Equations 6-4 and 6-8. In Equations 6-4 and 6-8, Lb for beam columns shall be taken as the actual unbraced length; the provisions in Sections 6.2.2 and 6.3.1.2 that Lb need not be taken less than the maximum permitted unbraced length based upon Pr and Mr shall not be applied. c) When torsional bracing is provided for flexure in combination with relative or nodal bracing for the axial force, the required strength and stiffness shall be combined or distributed in a manner consistent with the resistance provided by the element(s) of the actual bracing details.
January 2010
Aluminum Design Manual
PART II Specification for Aluminum Structures Commentary
II Specification for Aluminum Structures Commentary TABLE OF CONTENTS Chapter A General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.2 Referenced Documents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.3 Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.3.1 General Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.3.1.1 Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.3.1.2 Temperature Limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.3.1.3 Tension Coefficient kt. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.3.2 Wrought Products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 A.3.3 Castings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 A.3.4 Filler Metal for Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 A.3.5 Bolts and Nuts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 A.3.6 Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 A.3.7 Screws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Chapter B Design Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.1 Section Properties (2.1, 4.9.1, 7.2.1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.2 Loads and Load Combinations (2.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.2.1 Building-Type Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.2.2 Bridge-Type Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.2.3 Other Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.3 Design Basis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.3.1 Limit States. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.3.2 Required Strength (2.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 B.3.2.1 Design for Strength Using Load and Resistance Factor Design (LRFD). . . . . . . . . . . 12 B.3.2.2 Design for Strength Using Allowable Strength Design (ASD) . . . . . . . . . . . . . . . . . . . 13 B.3.3 Design for Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.3.4 Design for Serviceability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.3.5 Design for Fatigue. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.3.6 Design for Fire Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.3.7 Design of Braces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B.4 Buckling Constants (3.3) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 B.5 Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 B.5.1 Width of Flat Elements and Stiffeners (3.4.8, 3.4.8.1, 3.4.9, 3.4.9.1, 3.4.9.2) . . . . . . . . . . . . . . . 15 B.5.2 Radius of Curved Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 B.5.3 Thickness of Elements (4.12) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 B.5.4 Strength of Elements in Uniform Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 B.5.4.1 Flat Elements Supported on One Edge (3.4.8, 3.4.8.1, 3.4.15). . . . . . . . . . . . . . . . . . . 15 B.5.4.2 Flat Elements Supported on Both Edges (3.4.9, 3.4.16). . . . . . . . . . . . . . . . . . . . . . . . 16 B.5.4.3 Flat Elements Supported on One Edge and with a Stiffener on the Other Edge (3.4.9.1, 3.4.16.2). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 B.5.4.4 Flat Elements Supported on Both Edges and with an Intermediate Stiffener (3.4.9.2, 3.4.16.3). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 B.5.4.5 Curved Elements Supported on Both Edges (3.4.10, 3.4.16.1). . . . . . . . . . . . . . . . . . . 16 B.5.4.6 Flat Elements Alternate Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 B.5.5 Strength of Elements in Flexure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 B.5.5.1 Flat Elements Supported on Both Edges (3.4.18). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 B.5.5.2 Flat Elements Supported on Tension Edge, Compression Edge Free (3.4.17). . . . . . . 17 B.5.5.3 Flat Elements Supported on Both Edges and with a Longitudinal Stiffener (3.4.19, 4.5). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 B.5.5.4 Flat Elements Alternate Method (4.13). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 B.5.6 Elastic Buckling Stress of Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 January 2010
II-3
B.6 Fabrication and Erection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 B.7 Evaluation of Existing Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Chapter C Design for Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 C.1 General Stability Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 C.2 Calculation of Required Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 C.3 Calculation of Available Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Chapter D Design of Members for Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 D.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 D.2 Tensile Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 D.3 Area Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 D.3.1 Net Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 D.3.2 Effective Net Area. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Chapter E Design of Members for Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 E.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 E.2 Effective Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 E.3 Member Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 E.3.1 Flexural Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 E.3.2 Torsional and Flexural-Torsional Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 E.4 Local Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 E.4.1 Weighted Average Local Buckling Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 E.4.2 Alternate Local Buckling Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 E.5 Interaction Between Member Buckling and Local Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 E.6 Welded Compression Members. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 E.6.1 Compression Members with Transverse Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 E.6.2 Compression Members with Longitudinal Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Chapter F Design of Members for Flexure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 F.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 F.1.1 Bending Coefficient Cb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 F.1.1.1 Doubly Symmetric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 F.1.1.2 Singly Symmetric Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 F.2 Open Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 F.2.1 Lateral-Torsional Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 F.2.2 Effective Radius of Gyration rye . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 F.2.2.1 Shapes Symmetric About the Bending Axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 F.2.2.2 Singly Symmetric Shapes Unsymmetric About the Bending Axis. . . . . . . . . . . . . . . . 26 F.2.2.3 Shapes Unsymmetric About the Bending Axis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 F.2.3 Interaction Between Local Buckling and Lateral-Torsional Buckling. . . . . . . . . . . . . . . . . . . . . 27 F.3 Closed Shapes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 F.3.1 Lateral-Torsional Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 F.4 Rectangular Bars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 F.4.1 Yielding and Rupture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 F.4.2 Lateral-Torsional Buckling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 F.5 Single Angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 F.5.1 Bending About Geometric Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 F.5.2 Bending About Principal Axes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 F.6 Pipes and Round Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 F.6.1 Yielding and Rupture. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 F.6.2 Local Buckling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 F.7 Rods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.8 Elements of Flexural Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.8.1 Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.8.1.1 Elements in Uniform Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.8.1.2 Elements in Flexure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 II-4
January 2010
F.8.2 Compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.8.2.1 Elements in Uniform Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.8.2.2 Elements in Flexure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.8.2.3 Alternate Compressive Flexural Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.8.3 Weighted Average Flexural Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.9 Welded Flexural Members. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.9.1 Flexural Members with Transverse Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 F.9.2 Flexural Members with Longitudinal Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 Chapter G Design of Members for Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 G.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 G.2 Members with Flat Webs Supported on Both Edges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 G.3 Round or Oval Tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Chapter H Design of Members for Combined Forces and Torsion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 H.1 Members Subject to Flexure and Axial Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 H.2 Members Subject to Torsion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 H.2.1 Round or Oval Tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 H.2.2 Rectangular Tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 H.2.3 Rods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 H.3 Members Subject to Torsion, Flexure, Shear, and/or Axial Compression. . . . . . . . . . . . . . . . . . . . . . . . . 32 H.3.1 Flat Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 H.3.2 Curved Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Chapter I reserved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter J Design of Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.1.1 Design Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.1.2 Fasteners in Combination with Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.1.3 Maximum Spacing of Fasteners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2 Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.1 Groove Welds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.1.1 Complete Penetration and Partial Penetration Groove Welds. . . . . . . . . . . . . . . . . . . . 33 J.2.1.2 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.1.3 Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.2 Fillet Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.2.1 Effective Throat and Effective Length. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.2.2 Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.3 Plug and Slot Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.3.1 Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.2.3.2 Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.2.4 Stud Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.2.5 Post-Weld Heat Treating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.3 Bolts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.3.1 Bolt Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 J.3.2 Holes and Slots for Bolts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 J.3.3 Minimum Spacing of Bolts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 J.3.4 Minimum Edge Distance of Bolts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 J.3.5 Bolt Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 J.3.6 Bolt Shear . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 J.3.7 Bolt Bearing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 J.3.8 Slip-Critical Bolted Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 J.3.8.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 J.3.8.2 Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 J.3.8.3 Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 J.3.8.4 Design for Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 January 2010
II-5
J.4
J.5
J.6
J.7 J.8
J.9
J.3.8.5 Design for Slip Resistance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 J.3.8.6 Washers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 J.3.9 Lockbolts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.3.10 Long Grips. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.4.1 Rivet Material . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.4.2 Holes for Cold-Driven Rivets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.4.3 Minimum Spacing of Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.4.4 Minimum Edge Distance of Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.4.5 Rivet Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.4.6 Rivet Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.4.7 Rivet Bearing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.4.8 Blind Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.4.9 Hollow-End (Semi-Tubular) Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tapping Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.5.1 Screw Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.5.2 Holes for Screws. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.5.3 Minimum Spacing of Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.5.4 Minimum Edge Distance of Screws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.5.5 Screwed Connection Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J.5.5.1 Pull-Out. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 J.5.5.1.1 Screws in Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 J.5.5.1.2 Screws in Screw Slots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 J.5.5.2 Pull-Over. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 J.5.5.3 Screw Tension. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 J.5.6 Screwed Connection Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.5.6.1 Screw Bearing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.5.6.2 Screw Tilting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.5.6.3 Screw Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Affected Elements of Members and Connectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.6.1 Strength of Connectors in Tension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.6.2 Strength of Connectors in Shear. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.6.3 Block Shear Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.6.4 Strength of Connectors in Compression. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bearing Strength of Flat Surfaces and Pins. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Flanges and Webs with Concentrated Forces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.8.1 Crippling of Flat Webs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.8.2 Bearing Stiffeners . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.8.3 Combined Crippling and Bending of Flat Webs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Roofing and Siding Connections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 J.9.1 Endlaps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.9.2 Sidelaps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J.9.3 Fasteners in Laps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Chapter K reserved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chapter L Design for Serviceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 L.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 L.2 Camber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 L.3 Deflections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 L.4 Vibration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 L.5 Wind-Induced Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 L.6 Expansion and Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 L.7 Connection Slip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Chapter M Fabrication and Erection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.1 Layout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.1.1 Punch and Scribe Marks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.1.2 Temperature Correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . II-6
January 2010
M.2 Cutting. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.2.1 Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.2.2 Edge Quality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.2.3 Re-entrant Corners. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.3 Heating. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.4 Holes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.4.1 Fabrication Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.4.2 Hole Alignment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M.5 Bending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.6 Finishes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.6.1 Where Protective Coating Is Required . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.6.2 Surface Preparation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.6.3 Abrasion Blasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.7 Contact with Dissimilar Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 M.7.1 Steel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 M.7.2 Wood, Fiberboard, or Other Porous Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 M.7.3 Concrete or Masonry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 M.7.4 Runoff from Heavy Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 M.8 Fabrication Tolerances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 M.9 Welding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 M.10 Bolt Installation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 M.11 Riveting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 M.11.1 Driven Head. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 M.11.2 Hole Filling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 M.11.3 Defective Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M.12 Erection Tolerances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 Appendix 1 Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.2 Test Loading and Deflections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 Number of Tests and the Evaluation of Test Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.3.1 Tests for Determining Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.3.2 Tests for Determining Structural Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.4 Testing Roofing and Siding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 1.4.1 Test Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.2 Different Thicknesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.3 Design and Allowable Strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4.4 Deflections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 2 reserved. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 3 Design for Fatigue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.2 Constant Amplitude Loading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 3.3 Variable Amplitude Loading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Appendix 4 Design for Fire Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.1.1 Definitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.2 Performance Objectives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.3 Load Combinations and Required Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2 Design for Fire Conditions by Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.1 Design-Basis Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1.1 Localized Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1.2 Post-Flashover Compartment Fires. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1.3 Exterior Fires. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1.4 Fire Duration. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1.5 Active Fire Protection Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . January 2010
II-7
4.2.2 Temperatures in Structural Systems under Fire Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.3 Material Properties at Elevated Temperatures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.3.1 Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.3.2 Thermal Expansion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.3.3 Specific Heat. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 4.2.4 Structural Design Requirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4.1 General Structural Integrity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4.2 Strength Requirements and Deformation Limits. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4.3 Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4.3.1 Advanced Methods of Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4.3.2 Simple Methods of Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.4.4 Design Strength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Design by Qualification Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.1 Qualification Standards. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3.2 Restrained Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 5 Evaluation of Existing Structures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Material Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Wrought and Cast Products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Welds. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Bolts and Rivets. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 Evaluation by Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.2 Strength Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.3 Serviceability Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Evaluation by Load Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 5.5 Evaluation Report. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 6 Design of Braces for Columns and Beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.1 General Provisions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.1.1 Bracing Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1.2 Bracing Orientation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Column Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.2.1 Relative Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.2 Nodal Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3 Beam Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.3.1 Lateral Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1.1 Relative Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.1.2 Nodal Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2 Torsional Bracing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3.2.1 Nodal Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 6.3.2.2 Continuous Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 Beam-Column Bracing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .50
II-8
January 2010
Chapter A General Provisions A.1 Scope This Specification replaces the 2005 Specification for Aluminum Structures—Allowable Stress Design and the 2005 Specification for Aluminum Structures—Building Load and Resistance Factor Design, and its organization is similar to the 2010 AISC Specification for Structural Steel Buildings. This Specification provides the nominal strength of aluminum structures, members, and connections. The nominal strength is usually defined as a force or moment, but in some cases as a stress. This Specification provides two methods of design: 1) Load and Resistance Factor Design (LRFD): The nominal strength multiplied by a resistance factor must equal or exceed the required strength determined by analysis for the appropriate LRFD load combinations. This Specification provides resistance factors for buildingtype structures; 2) Allowable Strength Design (ASD): The nominal strength divided by a safety factor must equal or exceed the required strength determined by analysis for the appropriate ASD load combinations. This Specification provides safety factors for building-type structures and bridge-type structures.
A.2 Referenced Documents This section lists the referenced documents and establishes the editions of the documents to be used with this Specification.
A.3 Material A.3.1 General Properties More precise densities and coefficients of thermal expansion than those given in this Section are given in the Aluminum Design Manual Part IV Tables 7 and 8, respectively, and in Aluminum Standards and Data. The shear yield strength _Fsy is based on the von Mises yield criterion that Fsy = Fty /√3, approximated as Fsy = 0.6 Fty. A.3.1.1 Mechanical Properties For the alloys included in this Specification, mechanical properties are negligibly affected at temperatures up to 200°F. The Aluminum Design Manual Part IV Table 9 and Kaufman (1999) provide typical mechanical properties for many aluminum products at elevated temperatures. The reduction in strength varies with alloy, temper, temperature, and time of exposure. Because the reduction in strength will not exceed 5% for the alloys, tempers, times, and temperatures given in Table A.3.2, it is unnecessary to account for this reduction in design within these limits. January 2010
A.3.1.2 Temperature Limits See the commentary to Section M.3. A.3.1.3 Tension Coefficient kt The notch strength is the ultimate tensile strength of a standard notched specimen. Kaufman (2001) documented the notch strength of a number of aluminum alloy-tempers and suggested ASTM tests for determining notch strength. Alloy-tempers with notch-strength-to-yield-strength ratios less than 1 are considered to be notch sensitive, since they will rupture at a notch before yielding. Such alloytempers require a reduction in the tensile ultimate strength used for design. This reduction is made by dividing the tensile ultimate strength by the tension coefficient kt, a coefficient greater than or equal to 1. The kt factor of 1.25 for 2014-T6 has been used since publication of ASCE (1956). The kt factor of 1.25 for 6005-T5 and 6105-T5 is based on the fact that Kaufman (2001) shows that the unit propagation energy for 6005-T5 is no greater than that for 2014-T6.
A.3.2 Wrought Products Table A.3.4 tensile ultimate strengths Ftu and tensile yield strengths Fty are specified strengths (Aluminum Association (2009)) except Fty for 1100-H12 and H14 rod and bar and drawn tube, Alclad 3003-H18 sheet, and 5050-H32 and H34 rod and bar, which are expected strengths, explained in the next paragraph. Specified strengths are established after sufficient test data have been accumulated to determine the form of the frequency distribution curve and to provide a reliable estimate of the population mean and standard deviation. In most instances the distribution is normal and strengths are based on the results of at least 100 tests from at least 10 different lots of material. Tensile strengths are established at levels at which 99% of the material is expected to conform at a 0.95 confidence level. Table A.3.4 compressive yield strengths Fcy and shear ultimate strengths Fsu are expected strengths that 99% of the population is expected, but not guaranteed, to equal or exceed. Material should not be accepted or rejected based on these strengths. These strengths are derived strengths established by multiplying strengths from tests of representative lots of material by the ratio of the specified tensile yield or ultimate strength to the tensile yield or ultimate strength of the lot tested. Effort is made to base these strengths on test results for at least 5 lots of each alloy, temper, and product, but there are instances where insufficient data are available and the strengths are based on data for similar products. II-9
Test methods used to determine mechanical properties are summarized below: Type of Stress
ASTM Test Method
Tension Compression Shear
B 557 E9 B 769
The compressive modulus of elasticity E given in Table A.3.4 is a typical value. The tensile modulus of elasticity is approximately 2% less than the compressive modulus. Aluminum alloys gain strength by heat treatment or strain hardening. Welding causes local annealing, which erases this strength increase in a zone along both sides of the weld. The resulting variation in mechanical properties in the vicinity of a weld is illustrated by the typical distribution in Figure CA.3.1. Moore, et al. (1971) discussed the effect of welding heat on aluminum mechanical properties. Table A.3.5 gives the welded strengths for weldments produced in accordance with AWS D1.2. The welded tensile ultimate strengths Ftuw are the weld qualification strengths required by AWS D1.2. Welded yield strengths are for 0.2% offset in a 2 in. (50 mm) gauge length. The 2 in. gauge length is centered on a transverse groove-welded specimen. Since the heat-affected zone extends approximately 1 in. from the center of a weld, the full specimen is heat-affected and thus representative of welded material. Welded compressive yield strengths Fcyw and welded shear ultimate strengths Fsuw are derived from the relationships among those properties of the base metal alloy/temper products. For non-heat treatable alloys, the welded tensile ultimate strengths Ftuw and welded tensile yield strengths Ftyw are the strengths for the annealed temper (O) of the alloy, and for heat treatable alloys, the welded tensile ultimate and
Figure CA.3.1 DISTRIBUTION OF MECHANICAL PROPERTIES NEAR A WELD II-10
tensile yield strengths are slightly less than the solution heat treated (T4 temper) strengths (Nelson and Howell (1952)). For heat treatable alloys, the welded tensile ultimate and welded tensile yield strengths are based on statistical analysis of test data where possible, and are the strengths that 99% of the population would be expected to equal or exceed with a confidence level of 0.75. Where insufficient data are available, welded strengths are based on data for combinations of similar filler and base metal.
A.3.3 Castings ASTM B 26 and B 108 do not specify tensile yield strengths for some of the cast alloy-tempers they include (for example, sand cast 356.0-T7). These alloy-tempers are not included in Table A.3.6 (and therefore are excluded from the scope of this Specification) since design usually uses the yield strength. There are also other alloy-tempers in B 26 or B 108 that are not included in Table A.3.6 and therefore not included in this Specification. ASTM B 26 and B 108 do not require conformance with dimensional standards (tolerances) as do ASTM specifications for wrought products (for example, B 209). Therefore, dimensional standards for castings are established in this Specification as those in the Aluminum Association Standards for Aluminum Sand and Permanent Mold Castings. The strengths specified in ASTM B 26 Table 2 for sand castings are for separately cast test bars and not for the castings themselves. Section 11.3 of ASTM B 26 states “When specified, the tensile strength, yield strength, and elongation values of specimens cut from castings shall not be less than 75% of the tensile and yield strength values and not less than 25% of the elongation values specified in Table 2.” Therefore, the strengths given in Table A.3.6 are based on 75% of the ASTM B 26 Table 2 strengths to represent what a purchaser would expect to receive if he requires testing of the actual castings. Castings are more prone to discontinuities than wrought products. Therefore, this Specification includes discontinuity standards for castings in order for them to be designed to the same Specification provisions as wrought products. The quality standards are based on the following: ASTM B 26 and B 108 (section 20) both include options for liquid penetrant and radiographic inspection that may be specified by the purchaser. Liquid penetrant inspection detects only surface flaws, so it is insufficient. ASTM B 26 and B 108 only require radiographic inspection be performed if the purchaser specifies such inspection. If such inspection is specified, the purchaser must also specify which of four quality grades (A, B, C, or D) must be met. Grade A allows no discontinuities at all; this is more stringent than wrought product quality levels and so it is unwarranted. When Grade D is specified, no tensile tests of coupons cut from castings are required. Therefore, only grade B or C are suitable for the type of structural components addressed by this Specification. Grade C is used, since Grade C allows gas holes no larger than approxiJanuary 2010
mately 1/8 in. and this is the same as the ultrasonic inspection Grade B flaw size limit for wrought plate in Aluminum Standards and Data (Table 6.3). Once the acceptance criteria for an individual casting are determined, the number of castings from a given lot to be radiographed and the acceptance criteria for the lot must be established. Standards for Aluminum Sand and Permanent Mold Castings establishes four frequency levels for inspection, Level 1 requiring the most frequent inspection (radiographing every casting). Inspection Level 2 requires a statistically determined frequency of sampling and is used in this Specification. Level 3 leaves the inspection frequency up to the foundry and Level 4 requires no radiographs; therefore, neither requires inspection. Strengths given in Table A.3.6 and Table A.3.6M are taken from ASTM B 26 for sand castings and B 108 for permanent mold castings. B 26 allows the purchaser to require that the strength of coupons cut from production castings be no less than 75% of the specified strength, so the values in Table A.3.6 are the B 26 values factored by 0.75. B 108 has the same requirement, but for certain alloytempers allows the purchaser to specify either 1) locations in the casting that shall have certain B 108-specified tensile strengths; or 2) that any location in the casting shall have certain B 108-specified tensile strengths. The strengths for case 2) are usually lower than those for case 1). For
January 2010
both cases 1) and 2), the strengths in Table A.3.6 are the B 108-specified strengths without any factors. Kaufman (2001) Figure 5.4 provides notch-strength-toyield-strength ratios for various sand and permanent mold alloy/temper products. The alloy/temper products in this Specification have notch-yield ratios ≥ 1.0, so no reduction in tensile fracture strength is required for notch sensitivity for these alloy-tempers and the tension coefficient kt is 1.0.
A.3.4 Filler Metal for Welding This Specification and AWS D1.2 require that weld filler metal comply with AWS A5.10. Tables M.9.1 and M.9.2 show the appropriate filler alloy for various base metal combinations.
A.3.5 Bolts and Nuts This Specification addresses only aluminum bolts.
A.3.6 Rivets This Specification addresses only aluminum rivets.
A.3.7 Screws This Specification addresses only aluminum screws. There are no ASTM specifications for aluminum screws.
II-11
Chapter B Design Requirements B.1 Section Properties
B.2 Loads and Load Combinations
Section properties for many shapes are given in this Manual in Part V. Formulas for calculating section properties are also given in Part V. Nominal (rather than minimum) dimensions are used to calculate section properties. This is because safety or resistance factors account for the fact that actual dimensions may be less than nominal dimensions, within the tolerances prescribed by the material specifications required by Section A.3. The torsion constant J may be determined as follows:
B.2.1 Building-Type Structures
a) For open shapes J = S (1/3 - 0.2t/b)bt3 for the rectangles comprising the shape where b is the larger dimension and t is the smaller dimension of each rectangle. The term for rectangles with b/t > 10 may be approximated by bt3/3. 4A2 m t b) For closed shapes of uniform thickness, J = ____ where s Am = the mean of the areas between the inner and outer boundaries, s is the length of the boundary at midthickness, and t is the boundary thickness. For rectangular tubes with side dimension a with thickness t1 and side dimension b with thickness t2 (see Figure CB.1.1) 2t2t1(a – t2)2 (b – t1)2 J = ________________ -t )+ t2(a t1(b – t1) 2 2t(a – t) (b – t) . If t1 = t2 = t, J = ________________ 2
2
a + b – 2t
c) For shapes containing open parts and closed parts, J is the sum of J for the open parts and J for the closed parts.
For building-type structures, ASCE 7 Section 2.3 provides LRFD load combinations and ASCE 7 Section 2.4 provides ASD load combinations.
B.2.2 Bridge-Type Structures Aluminum highway bridges may also be designed using AASHTO (1991) for ASD and AASHTO (1998) for LRFD.
B.2.3 Other Structures Loads for structures other than building- and bridgetype structures may be determined from specifications that address such structures. For example, AASHTO’s Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals (2009) may be used to determine the loads for structures within its scope.
B.3 Design Basis Load and Resistance Factor Design (LRFD) and Allowable Strength Design (ASD) are equally acceptable in this Specification.
B.3.1 Limit States A limit state is a condition in which a structure or component is judged to be no longer useful for its intended service (serviceability limit state) or to have reached its ultimate load-carrying capacity (strength limit state). An example of a serviceability limit state is a deflection beyond which the structure is unfit for service. An example of a strength limit state is member buckling of a column.
B.3.2 Required Strength This Specification permits the use of elastic analysis only in determining required strengths. B.3.2.1 Design for Strength Using Load and Resistance Factor Design (LRFD)
Figure CB.1.1 CROSS-SECTIONAL NOTATION II-12
Design by LRFD requires that equation B.3-1 be satisfied; that is, the required strength determined from the LRFD load combinations does not exceed the design strength. The design strength fRn is the product of the resistance factor f and the nominal strength Rn. Resistance factors are less than or equal to 1.0 and account for unavoidable deviations of the actual strength from the nominal strength and for the manner and consequence of failure. The basis for load and resistance factor design is given by Ellingwood, et al. (1982). The resistance of the structure R and the load effect Q are modeled as statistically independent random quantities as shown in Figure CB.3.1. January 2010
Figure CB.3.1 SCHEMATIC REPRESENTATION OF PROBABILITIES OF THE LOAD EFFECT AND THE RESISTANCE Failure occurs when the resistance R is less than the load effect Q; the probability of this occurring is represented by the overlap between the two curves in Figure CB.3.1. This probability is a function of the difference between mean value of the resistance and the mean value of the load effect and the distribution shapes of the R and Q curves. Failure can also be defined as ln(R/Q) < 0. In Figure CB.3.2, failure is represented by the shaded area. The reliability index β is given by ln( Rm/Qm) _______ β = ___________ √V R2 + V Q2
where Rm = mean value of resistance Qm = mean value of load effect VR = coefficient of variation of resistance VQ = coefficient of variation of load effect. Galambos (1979) determined the reliability index for limit states in the Specifications for Aluminum Structures. His work is summarized in Tables CB.3.1, CB.3.2, and CB.3.3. Resistance factors in this Specification were chosen to achieve similar levels of safety and reliability for ASD and LRFD. To do so, the relationship between safety factors and resistance factors can be established as follows: For ASD: For LRFD:
Rn / W = D + L fRn = AD + BL
where A = dead load factor = 1.2 B = live load factor = 1.6. Solving for f φ = [A(D/L) + B] / [Ω(1 + D/L)] Table CB.3.4 shows that for D/L ratios of about 0.5 or less, resistance factors of 0.75 for rupture, 0.90 for all other January 2010
Figure CB.3.2 DEFINITION OF THE RELIABILITY INDEX ß member limit states, 0.65 for bolt or rivet failure, and 0.5 for screw failure are no less conservative than ASD; therefore, this Specification uses these resistance factors. This matches the 2005 AISC Specification for rupture and other member limit states. B.3.2.2 Design for Strength using Allowable Strength Design (ASD) The Specification for Aluminum Structures has historically used a safety factor of 1.65 on yield and beam buckling limit states and 1.95 on tensile rupture limit states, and those are used in this edition of the Specification. The safety factor for column member buckling in this Specification has effectively been 1.65, since a safety factor of 1.95 was prescribed without applying a factor for out-of-straightness, which is approximately 0.85 (1.95 × 0.85 = 1.65). Because a column out-of-straightness factor of 0.85 is applied in this edition of the Specification, the safety factor for column member buckling is set at 1.65. The safety factor for column local buckling has been changed in this edition of the Specification from 1.95 to 1.65 to be consistent with the safety factor for beam local buckling. An out-of-straightness factor has not been applied to local buckling because the local buckling strength is not sensitive to out-of-straightness (Sharp (1993)).
B.4 Buckling Constants The buckling constants given in Section B.4 are used to determine inelastic buckling strengths and reflect the tangent modulus of elasticity in the inelastic range, as documented by Clark and Rolf (1966). The stress-strain curve for artificially aged tempers (those beginning with T5, T6, T7, T8, or T9) has a different shape after yield than that for non-artificially aged tempers (those beginning with O, H, T1, T2, T3, or T4). Therefore, different buckling constant formulae are used for artificially aged tempers than those used for non-artificially aged tempers. II-13
Table CB.3.1 SUMMARY OF RELIABILITY INDEX STATISTICAL DATA Sec 3.4.*
Limit State
SF
Y U Y B Y IB EB Y B Y IB EB Y B Y IB EB
1.65 1.95 1.65 1.95 1.65 1.95 1.95 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65 1.65
1,2,3,4 1,2,3,4 8,9 8,9 10 10 10 11,13,14 11,13,14 12,16.1 12,16.1 12,16.1 15,16,17 15,16,17 20 20 20
Pm
1.0 1.0 1.0 1.0 1.0 1.0 1.24 1.0 1.03 1.0 1.01 1.24 1.0 1.0 1.0 1.07 0.93
Mm
Fm
1.10 1.10 1.10 1.0 1.10 1.0 1.0 1.10 1.0 1.10 1.0 1.0 1.10 1.0 1.10 1.0 1.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
Rm/Rn
VP
VM
VF
VR
Category
1.10 1.10 1.10 1.0 1.10 1.0 1.24 1.10 1.03 1.10 1.01 1.24 1.10 1.0 1.10 1.07 0.93
0 0 0 0.05 0 0.05 0.27 0 0.11 0 0.05 0.27 0 0.05 0 0.09 0.09
0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06
0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05
0.08 0.08 0.08 0.09 0.08 0.09 0.28 0.08 0.13 0.08 0.09 0.28 0.08 0.09 0.08 0.12 0.12
A B C D C D E C F C G H C I C J K
*Section number in Specification for Aluminum Structures, 2005. Notes: 1. Limit states are: Y = yield; U = tensile rupture; B = buckling; IB = inelastic buckling; EB = elastic buckling. 2. Parameters are: SF = safety factor Pm = mean value of the ratio of actual strength to theoretical strength Mm = mean value of the ratio of material strength to specified material strength Fm = mean value of the ratio of fabricated dimensions to nominal dimensions Rm/Rn = Pm Mm Fm VP = coefficient of variation of the ratio of actual strength to theoretical strength VM = coefficient of variation of the ratio of material strength to specified material strength VF = coefficient of variation of the ratio of fabricated dimensions to nominal dimensions __________ VR = √VP2 + VM2 + VF2.
Table CB.3.2 LIMIT STATE CATEGORIES Category
SF
Rm/Rn
VR
A B C D E F G H I J K
1.65 1.95 1.65 1.95 1.95 1.65 1.65 1.65 1.65 1.65 1.65
1.10 1.10 1.10 1.00 1.24 1.03 1.01 1.24 1.00 1.07 0.93
0.08 0.08 0.08 0.09 0.28 0.13 0.09 0.28 0.09 0.12 0.12
Description yield in tension rupture in tension yield in compression local buckling in columns elastic local buckling of curved elements in compression lateral torsional buckling of beams inelastic local buckling of curved elements in bending elastic local buckling of curved elements in bending local buckling in beams inelastic shear buckling elastic shear buckling
Table CB.3.3 RELIABILITY INDICES Category A B C D E F G H I J K
II-14
b for D/L = 0.1
b for D/L = 0.2
2.46 3.16 2.87 2.72 2.44 2.01 2.08 1.98 2.04 2.20 1.65
2.64 3.40 3.09 2.92 2.51 2.13 2.22 2.03 2.18 2.34 1.75
Description yield in tension rupture in tension yield in compression local buckling in columns elastic local buckling of curved elements in compression lateral torsional buckling of beams inelastic local buckling of curved elements in bending elastic local buckling of curved elements in bending local buckling in beams inelastic shear buckling elastic shear buckling
January 2010
Table CB.3.4 RELATING RESISTANCE FACTORS TO SAFETY FACTORS Dead-to-live load ratio
D/L
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
dead load factor live load factor
A B
1.2 1.6
1.2 1.6
1.2 1.6
1.2 1.6
1.2 1.6
1.2 1.6
1.2 1.6
1.2 1.6
1.2 1.6
W f
1.95 0.82
1.95 0.80
1.95 0.79
1.95 0.77
1.95 0.76
1.95 0.75
1.95 0.74
1.95 0.74
1.95 0.73
W f
1.65 0.97
1.65 0.95
1.65 0.93
1.65 0.91
1.65 0.90
1.65 0.89
1.65 0.88
1.65 0.87
1.65 0.86
W f
2.34 0.68
2.34 0.67
2.34 0.66
2.34 0.64
2.34 0.63
2.34 0.63
2.34 0.62
2.34 0.61
2.34 0.61
W f
3.00 0.53
3.00 0.52
3.00 0.51
3.00 0.50
3.00 0.50
3.00 0.49
3.00 0.48
3.00 0.48
3.00 0.47
Limit state: rupture safety factor resistance factor All other member limit states safety factor resistance factor Limit state: bolt, rivet failure safety factor resistance factor Limit state: screw failure safety factor resistance factor
The weld-affected zone in non-heat treatable alloys has the annealed (O) temper strength, and the weld-affected zone in heat-treatable alloys has a strength slightly less than the solution heat-treated (T4) temper. For this reason, buckling constants for weld-affected zones of all alloys are determined from Table B.4.1, which applies to O and T4 temper material.
linearly tapered thickness elements with d ≤ 2.0 (i.e., tmax ≤ 3tmin). The tapered flanges of American Standard channels and American Standard I beams meet this criterion. Three types of edge supports for elements with tapered thickness are addressed in Section B.5.3:
B.5 Elements
a) Tapered thickness elements with the thick edge supported and the thin edge free (Figure CB.5.1(a)): For such elements, it is conservative to use b/tavg for the slenderness ratio. Using b/tavg gives a slenderness ratio that is conservative by as much as 28% compared to finite element analysis for d = 2. Section B.5.3a provides an approximate expression for the slenderness ratio that is less conservative and more accurate than using b/tavg. b) Tapered thickness elements with the thin edge supported and the thick edge free (Figure CB.5.1(b)): For such elements, the slenderness ratio can be approximated b by (1.02) ___ tavg . Using b/tavg understates the slenderness ratio by only 3% compared to finite element analysis, so this Specification allows the use of b/tavg. c) Tapered thickness elements supported on both edges (Figure CB.5.1(c)): The slenderness ratio can be approximated
B.5.1 Width of Flat Elements and Stiffeners If the inside corner radius exceeds 4 times the element thickness, the inside radius is taken as 4 times the thickness in calculating the element width. This rule is arbitrary but deemed reasonable.
B.5.2 Radius of Curved Elements The mid-thickness radius of curved elements is used to determine their slenderness to be consistent with the work by Clark and Rolf (1964).
B.5.3 Thickness of Elements Kim (2003) provided the method used in this Section for determining the slenderness ratio for members that have
( )
Figure CB.5.1 January 2010
II-15
( )
b by (1.02 + 0.02δ) ___ t . Using b/tavg under states the slender
ness ratio by at most only 5% compared to finite element analysis, so this Specification allows the use of b/tavg.
avg
Once the slenderness ratio has been determined, use the Specification Section for a constant thickness element with the same edge conditions to determine the strength of the element.
B.5.4 Strength of Elements in Uniform Compression The strength of elements in uniform compression is the weighted average of the strengths of the unwelded and weldaffected zones of the element. The strength of elements with transverse welds is not limited by yielding because yielding at a transverse weld does not cause an appreciable change in length. The weld-affected zone for transverse welds that extend across the full width of an element is the gross area of the element. B.5.4.1 Flat Elements Supported On One Edge Sooi and Peköz (1993) determined the post-buckling strength given in Section B.5.4.1 for slenderness ratios greater than S2. Using the buckling coefficient k = 0.425 for an element with one edge simply supported and the other free from Galambos (1998) Figure 4.2 and n = 0.33 (see Section A.3.1), the elastic buckling stress can be determined as 2 0.425π2E π E kπ2E Fe = ___________ = ______________ 2 2 = __________ 2 2 12(1-v )(b/t) 12(1-0.33 )(b/t) 25.16(b/t)2 2 π E = ________ 2 (5.02b/t)
In columns buckling about a principal axis that is not an axis of symmetry (for example, channels buckling about the weak axis), the centroid of the stresses may not be the same as that for the full section. This is due to the nonlinear post-buckling stress distribution in the section’s elements. Although some post-buckling strength may exist, it may not be as large as that if the buckling axis were an axis of symmetry. Therefore, this Section limits the strength in such cases to the elastic local buckling strength. B.5.4.2 Flat Elements Supported on Both Edges Using the buckling coefficient k = 4.00 for an element simply supported on both edges from Galambos (1998) Figure 4.2 and n = 0.33 (see Section A.3.1), the elastic buckling stress is: 2 kπ2E 4.00π2E π E Fe = ___________ = _______________ = _________ 2 2 2 2 12(1-v )(b/t) 12(1-0.33 )(b/t) 2.673(b/t)2 2 π E = ________ (1.64b/t)2
II-16
Jombock and Clark (1968) determined the post-buckling strength given in Section B.5.4.2 for slenderness ratios greater than S2. B.5.4.3 Flat Elements Supported on One Edge and with a Stiffener on the Other Edge The study by Sooi and Peköz (1993) used to establish these provisions was based on sheet metal shapes where the thickness of the stiffener is the same as the thickness of the stiffened element, and these provisions give the same result regardless of the stiffener thickness. Therefore, this Specification requires that the stiffener be at least as thick as the element to be stiffened. The denominator in each of Equations B.5-3 and B.5-4 for rST is the radius of gyration of a stiffener adequate to give the element being stiffened the strength of an element supported on both longitudinal edges (Ra). Sooi and Peköz adapted the equations for Ra from the AISI Specification (1986) and compared them with the equation proposed by Sharp (1966). The elastic buckling analysis by Sharp shows that Ra = 6t. Elastic buckling begins at a b/t ratio equal to Se where Se is the limiting b/t ratio at which a stiffened element is fully effective. At this value of b/t, the value of Ra obtained from Equation B.5-3 matches the value derived by Sharp. A linear relationship is assumed between Ra and b/t if b/t is between Se /3 and Se. To develop post-bucking strength of the stiffened element, Ra is greater than 6t. An edge stiffened element with a b/t ratio exceeding Se has post-buckling strength. Equation B.5-4 addresses such cases, where b/t is between Se and 2Se. There is insufficient test data to develop an equation for Ra when b/t exceeds 2Se. The limitation on the Ds/b ratio prevents adverse interaction between local buckling of the edge stiffener and the stiffened element. Stiffening bulbs and other complex shapes may provide greater strengths than those provided for in Section B.5.4.3. Sharp (1993) gives a method for estimating the buckling strength for these other shapes. B.5.4.4 Flat Elements Supported on Both Edges and with an Intermediate Stiffener The provisions in this Section are based on Sharp (1966), who developed an equation for flat elements supported on both edges with multiple intermediate stiffeners. Sooi and Peköz (1993) found that these provisions, in conjunction with the weighted average method, gave good agreement with test strengths. B.5.4.5 Curved Elements Supported on Both Edges In theory, the elastic buckling strength of an ideal cylindrical shell loaded in compression can be determined by __
√ R
b substituting an equivalent slenderness ratio of 4.0 __ t into
January 2010
the column formula. The buckling strength of actual shells, however, is strongly affected by imperfections in the geometry and end conditions. Tests indicate that this effect tends to increase with increasing Rb/t. The effect of imperfections is taken into account by the formulas in this Section, which are conservative when compared with the results of numerous tests on tubes and cylinders (Clark and Rolf (1964), Weingarten, Morgan, and Seide (1965)). Section B.5.4.5 is based on elastic local buckling strength since severe deformations occur at this load. B.5.4.6 Flat Elements Alternate Method Strengths determined using the provisions of this Section agree well with the test strengths reported by Bijlaard and Fisher (1952) for I beams and square tubes. Sections B.5.4.1 through B.5.4.5 address the compressive strengths of beam elements assuming that the supported edges of elements are fixed against translation and free to rotate. Section B.5.4.6 provides an alternate method by which a more accurate assessment of element support conditions can be used to determine the compressive strength. The use of Section B.5.4.6 for welded members is prohibited because the accuracy of the alternate method given in Section B.5.4.6 has not been established for welded members. To determine Fe, the elastic buckling stress of the column with continuous lateral support, a linear elastic analysis such as the finite strip method, by which a member is divided into strips that run the length of the member, may be used.
B.5.5 Strength of Elements in Flexure The local buckling strength of elements in flexure is not affected by welds in the tension zone of the element. Therefore, only weld-affected zones in the compression portion of the element are considered in determining the local buckling strength of these elements. Further study is required to account for the effect of the location of the weld-affected zone, which is not addressed by the Specification. B.5.5.1 Flat Elements Supported on Both Edges The coefficients in the formula for inelastic buckling strength are assumed to be the same as for solid rectangular shapes (Section F.4). When the neutral axis is at the mid-height of the element, the equivalent slenderness ratio is 0.65b/t, which applies to an element in bending with both edges simply supported. Simple support is assumed because the boundary conditions at the compression edge are more important than those at the tension edge and compression elements supporting the compression flange may buckle at the same time as the web.
gular shapes (Section F.4). The equivalent slenderness ratio of 3.5b/t is based on partial restraint against rotation at the supported edge. Section B.5.5.2 is based on elastic buckling strength. This type of element is assumed to have negligible postbuckling strength. B.5.5.3 Flat Elements Supported on Both Edges and with a Longitudinal Stiffener The coefficients in the formula for inelastic buckling strength are assumed to be the same as for solid rectangular shapes (Section F.4). The equivalent slenderness ratio is 0.29b/t based on simple support at the edges and at the stiffener using theory from Bleich (1952). Section B.5.5.3 requires that a longitudinal stiffener on a beam web shall be located so that the distance from the toe of the compression flange to the stiffener’s centroid is 0.4 times the distance from the toe of the compression flange to the beam’s neutral axis. This is the optimum location for increasing the buckling strength of the web. The resulting strength of the web is based on Bleich (1952). The stiffener’s required moment of inertia is the same as that used in earlier ASCE specifications (1962a, 1962b), and agrees with tests by Rockey (1958). The factor a accounts for the effect of eccentricity for a stiffener on one side of the web only (Massonnet (1962)). B.5.5.4 Flat Elements Alternate Method Sections B.5.4 and B.5.5 address the compressive strengths of beam elements assuming that the supported edges of elements are fixed against translation and free to rotate. Section B.5.5.4 provides an alternate method by which a more accurate assessment of element support conditions can be used to determine the compressive strength. Kim (2003) showed that Section B.5.5.4 is also reasonably accurate for shapes not addressed by Sections B.5.4 and B.5.5 and composed entirely of flat elements, including those with single or multiple intermediate stiffeners. The use of Section B.5.5.4 for welded members is prohibited because the accuracy of the alternate method given in Section B.5.5.4 has not been established for welded members. When Section F.8.2.3 is used in combination with the weighted average strength method given in Section F.8.3, the strength of a stiffened element need not be limited to the strength of the stiffener since the elastic buckling strength determined is the strength of the entire section, accounting for all elements. To determine Fe, the elastic buckling strength of the beam with continuous lateral support, a linear elastic analysis such as the finite strip method, by which a member is divided into strips that run the length of the member, may be used.
B.5.5.2 Flat Elements Supported on Tension Edge, Compression Edge Free
B.5.6 Elastic Buckling Stress of Elements
The coefficients in the formula for inelastic buckling strength were assumed to be the same as for solid rectan-
The elastic buckling stress of elements is the elastic local buckling stress. Since elastic local buckling stresses
January 2010
II-17
are used for the design of both members for compression (Chapter E) and members for flexure (Chapter F), the table of elastic local buckling stresses is provided in Chapter B. The elastic local buckling stress Fe for elements supported on one edge and with a stiffener on the other edge is based on the effectiveness of the stiffener. When the stiffener 2 π E has no effectiveness, rST = 0 and Fe = _______ and when the (5.0b/t)2 2 π E stiffener is fully effective, rST = 1 and Fe = _______ (1.6b/t)2
The elastic buckling stress of elements in uniform compression is used to check the interaction between member buckling and local buckling for columns (Section E.5),
II-18
and the interaction of lateral-torsional buckling and flange buckling for single web beams (Section F.2.3). This interaction can only govern if postbuckling strength is used. Postbuckling strength is used in Sections B.5.4.1, B.5.4.2, and B.5.4.3.
B.6 Fabrication and Erection Section B.6 invokes Chapter M for fabrication and erection issues.
B.7 Evaluation of Existing Structures Section B.7 invokes Appendix 5 for the evaluation of existing structures.
January 2010
Chapter C Design for Stability C.1 General Stability Requirements Design for stability includes the analysis to determine required strengths as well as proportioning the members and connections so they have adequate available strength.
C.2 Calculation of Required Strengths The five factors listed in Section C.2 are the factors that must be accounted for in an accurate stability analysis of a structure. 1) The designer must determine whether connection deformations are significant and need to be considered. 2) Second-order effects are included in many structural analysis programs. To determine if a program properly includes second-order effects, the program’s results can be compared to the two benchmark problems given in the AISC 2005 Specification commentary to Section 7.3. Most structural analysis programs that purport to address second-order effects include P-D effects, but some do not include P-d effects. P-d effects must be included in determining the required strength of individual compression members. 3) The pattern of geometric imperfections should be similar to the anticipated buckled shape of the structure and to the displacements caused by loads. Since the Specification for Aluminum Structures does not establish erection tolerances, Section C.2 requires that the imperfections be the tolerances specified by the designer. For example, if the maximum out-of-plumbness requirement for the structure is specified as H/500, then the imperfection at the top of a column relative to its base is H/500 where H is the height of the column. Geometric imperfections could also be accounted for by applying equivalent notional loads to the structure that are a fraction of the gravity loads for nominally ver-
January 2010
tical and horizontal members. However, including the geometric imperfections in the analysis model is applicable to all structural configurations. 4) The factor for flexural stiffness tb due to inelasticity matches the factor used by AISC and ranges from 1.0 for Pr ≤ 0.5Py to 0 for Pr = Py. This can be addressed by using tbI in place of I in the analysis. 5) The 0.8 factor on member stiffness due to uncertainty in stiffness and strength is the product of the resistance factor for columns (0.90) and the reduction factor (0.85) on the buckling strength of slender columns. The 0.8 factor also accounts for additional softening under combined axial compression and bending of intermediate or stocky columns. This can be addressed by using 0.8E in place of E in the analysis. The effective length method is not included in Chapter C since a second-order analysis must be made to determine if the effective length method is appropriate, and the method in Section C.2 is more direct. Also, it is often quite difficult to properly determine effective lengths. However, since Section C.1 allows any elastic method, the effective length method can be used if properly applied. The reason for factoring ASD loads by 1.6 is that the structure may not behave linearly, which is why 2nd order analysis is performed. To produce the same overall result with ASD and LRFD, the ASD analysis must be done at the LRFD load level. Then, since ASD results are compared to ASD allowable stresses, the ASD results must be divided by 1.6.
C.3 Calculation of Available Strengths Bracing requirements given in Appendix 6 do not apply to bracing that is included in the structural analysis performed in accordance with Section C.2.
II-19
Chapter D Design of Members for Tension D.1 General Provisions The allowable tensile strength for building structures is the lesser of the two values that result from applying a safety factor of 1.65 to the yield strength of the gross section and 1.95 to the ultimate strength of the net section. The corresponding safety factors for bridge structures are 1.85 and 2.2. These factors match those in ASCE (1962a) and ASCE (1962b) and have been used in the Specification for Aluminum Structures since its first edition in 1967.
For staggered holes in shapes with different thickness elements (for example, staggered holes in a channel flange and web), the Specification does not address the thickness to be used to determine the net area from the net width based on the s2/4g rule. A possible approach in this instance is to use the weighted average thickness (weighted by the length of the failure path in a given element) (see Gaylord et al. (1992)). The effective width of punched holes is the hole diameter + 1/32 in. to account for break-out on the back side of the part that punching may cause.
D.2 Tensile Strength
D.3.2 Effective Net Area
The axial tensile strength is the lesser of 1) the yield strength of the gross section and 2) the ultimate (fracture) strength of the net section. This is because the net section usually exists over only a short portion of the overall length of the member, and the elongation of the member resulting from yielding across the net section is small. Thus, yielding on the net section is not a limit state. The strength of tension members with transverse welds is limited by the strength of the transverse weld. Transverse welds are welds with an axis perpendicular to the member axis. If the entire cross section of the member is weldaffected, the tensile strength is Ftuw Ae. Yielding at a transverse weld is not a limit state, because, in a similar manner as for yielding at the net section, the elongation of the member resulting from yielding across a transverse weld is small. Longitudinal welds are welds with an axis parallel to the member axis. Usually only part of the cross section of longitudinally welded members is weld affected. The strength of a cross section with only part of its area weld affected can be estimated by adding up the strength of the material in the weld-affected zone and the unaffected material outside this zone (Hill, et al. (1962)). Hill and Brungraber (1962) showed that for members with part of the section weld-affected, the strength is the sum of the strength of the weld-affected material and the strength of the non-weld-affected material.
May and Menzemer (2005) showed that the effective area in tension is less than the net area due to the non-uniform stress distribution across the section at the connection for angles, tees, and channels connected by some but not all of their elements. This is accounted for by using the net effective area to calculate the tensile stress in the section. Designers should not combine bending stress due to the connection eccentricity with axial stress on the net effective area since the effect of the eccentricity is accounted for in the net effective area determination. To determine the eccentricities:
A net= b - 2d + ___ t
a) For tees connected only by their flanges (Figure CD.3.3(a)), the eccentricity in the y direction is the distance from the outside face of the flange to the neutral axis of the tee parallel to the flange. The eccentricity in the x direction is zero. For I beams connected only by their flanges (Figure CD.3.3(b)), split the section at the neutral axis parallel to the flanges to create two tees. b) For channels connected only by their webs the eccentricities are as shown in Figure CD.3.4. c) For angles connected only by one leg, the eccentricity in one direction is the distance from the face of the connected leg to the neutral axis of the angle parallel to the connected leg (Figure CD.3.5(a)). The eccentricity in the other direction is determined from a section obtained by subtracting the portion of the connected leg outside the centerline of the fastener closest to the unconnected leg. The eccentricity is the distance perpendicular to the unconnected leg from the centerline of the fastener closest to the unconnected leg to the neutral axis of the remaining section (Figure CD.3.5(b)). d) For I beams connected only by the web, eccentricities are determined as shown in Figure CD.3.6.
where t is the thickness of the bar and d is the diameter of the hole. In Figure CD.3.2, the angle section is flattened out into a bar for the purpose of calculating the net section. The flattened width is a + b - t.
If there is only one row of bolts in the direction of load or the only weld has an axis perpendicular to the direction of load, the length of the connection L is zero and the net effective area is the net area of the connected elements.
D.3 Area Determination D.3.1 Net Area Figures CD.3.1 and CD.3.2 illustrate the notation of this Section. The net section area for the bar shown in Figure CD.3.1 is
(
II-20
s2 4g
)
January 2010
Figure CD.3.1 BAR IN TENSION
Figure CD.3.2 ANGLE IN TENSION
Figure CD.3.3
Figure CD.3.4 January 2010
II-21
Figure CD.3.5
Figure CD.3.6
II-22
January 2010
Chapter E Design of Members for Compression E.1 General Provisions Because column member buckling strength (E.3) does not account for an approximate 0.85 factor on strength due to standard tolerance on out-of-straightness, the safety factor for column member buckling for members designed using this Specification prior to 2010 was actually about (0.85)(1.95) = 1.66. Because the 2010 Specification includes the 0.85 factor in the column member buckling strength but the safety factor has changed from 1.95 to 1.65, column member buckling allowable strengths did not change in the 2010 Specification. In the 2010 Specification, the safety factor for column local buckling strength changed from 1.95 to 1.65 to make it consistent with the safety factor for local buckling of beams. Unlike member buckling, local buckling strengths need not be reduced for out-of-straightness since Sharp (1993) notes that “the practical plate with initial crookedness . . . has essentially the same strength as that for the perfectly flat plate.”
For very short columns, the compressive strength is the compressive yield strength. Such columns are sometimes referred to as stub columns, for which the limit state is yielding rather than buckling. This is addressed in Section B.5.4, where the local buckling strength is limited by the yield strength.
E.3.1 Flexural Buckling For flexural buckling, the slenderness ratio kL/r is the greater of the slenderness ratios taken about each of the principal axes of the member.
E.3.2 Torsional and Flexural-Torsional Buckling
Chapuis and Galambos (1982) addressed the effective length of aluminum columns as a factor k times the length of the column between lateral supports.
Section E.3.2 is similar to the AISC (2005) Section E4 for torsional and flexural-torsional buckling. Based on data provided by Abramson (1977), Sharp (1993) showed that the member buckling strength equations of Section E.3 can be used for torsional-flexural buckling if an equivalent slenderness ratio is defined. The equivalent slenderness ratio (kL/r)e is based on the elastic torsional-flexural buckling stress. For point-symmetric sections such as cruciforms, torsional buckling is the most likely mode of failure and Fe becomes equal to Fet.
E.3 Member Buckling
E.4 Local Buckling
The inelastic buckling formulas in this Section use the tangent modulus column formula:
The strength of elements with welds that are not along the element edges may have less strength than elements without welds for two reasons:
E.2 Effective Length
π2E t F= ______ (kL/r)2
where: F = column buckling stress Et = tangent modulus (slope of stress strain curve) corresponding to Fe kL = effective length of column r = least radius of gyration of column. In the elastic range, this formula is simply the Euler column formula, which gives the buckling strength for values of kL/r exceeding S2. For values of kL/r less than S2, Templin, et al. (1938) and Clark and Rolf (1966) showed that the tangent modulus formula is approximated closely by a straight line. Hill and Clark (1956) and Batterman and Johnson (1967) showed that load eccentricity and initial crookedness reduce the buckling strength. The 0.85 factor on inelastic and elastic member buckling accounts for these effects. Sharp (1993) showed that strength of a 6061-T6 column that is out-of-straight by standard mill tolerance is about 83% of the strength of a perfectly straight column. AISC (2005) addresses out-of-straightness in steel column member buckling with a 0.877 factor on buckling strength, and uses a safety factor of 1.67 for column buckling. January 2010
1) Welding reduces the yield and ultimate strength of the metal. This can be accounted for by using the welded yield strength and welded buckling constants to determine the element strength. 2) Welding may introduce distortions. AWS D1.2 Section 4.15.4 requires a flatness tolerance on welded webs of d/100, where d = web depth, and Section 4.15.5 requires a flatness tolerance of w/100 < 0.25 in. on welded flanges, where w = full width of the flange. For extrusions, Aluminum Standards and Data 2009 Table 11.8 requires a flatness tolerance of 0.4% to 1.4% of the width, depending on part thickness and width, being greater for thin parts and large widths. For sheet and plate, Aluminum Standards and Data 2009 Table 7.17 requires a flatness tolerance of 0.5% to 1.3% of the width. Since the flatness tolerances for unwelded mill products and welded parts are approximately the same, distortions are not greater in welded elements than unwelded elements, and their strengths should not differ because of distortions. Sharp (1993) Figure 7.9 shows that the compressive strength of longitudinally edge-welded elements is slightly less than the unwelded strength, and considerably greater II-23
than the all-welded strength. The flatness tolerance for the test specimens ranged from 0.1% to 0.7% of the width. Sharp noted that “Welds decreased the strength compared to unwelded plates but the decrease was not as much as that calculated for all-welded material”. Compressive tests on welded aluminum plates (Conley, et al. (1963)) have demonstrated that the welds have little effect on postbuckling strength. To account for the reduction in strength in the weld-affected zone, a weighted average method is used.
E.4.1 Weighted Average Local Buckling Strength Crocket (1942) showed that the local buckling strength of a member is the sum of the local buckling strength of the member’s elements. The compressive strength of portions of a column at the intersection of elements (for example, at the web-flange juncture in a channel) is taken as Fcy since this material does not buckle locally and is not included in the area of the flange element or the web element.
E.4.2 Alternate Local Buckling Strength The alternate method for determining the local buckling stress is described in Section B.5.4.6.
E.5 Interaction Between Member Buckling and Local Buckling Sections B.5.4.1 and B.5.4.2 take advantage of the postbuckling strength of certain types of elements, because such elements may buckle elastically without causing failure of the member. However, if the local buckling stress of the section is less than the member buckling strength of the column, the reduced stiffness that accompanies local buckling may reduce the member buckling strength. Sharp (1970) developed the strength equation given in Section E.5 to address this interaction between member buckling and local buckling. Sharp’s equation agrees well with the results of compression tests on H-section and box section columns with thin elements reported by Bijlaard and Fisher (1952). The interaction between member buckling and local buckling is more likely to govern the strength when member buckling is elastic and an element of the member has a high slenderness ratio. The elastic local buckling strengths given in Table B.5.1 are accurate for square tube shapes and conservative for
II-24
other shapes. These values can be quite conservative for sections with elements whose edge restraint is more rigid than an element that is simply supported. Section E.4.2 provides a more accurate and less conservative method to determine the strength in such cases.
E.6 Welded Compression Members Brungraber and Clark (1962) investigated the strength of welded aluminum compression members. Welding can affect a member’s compression strength by reducing strength in the heat-affected zone, causing residual stresses, and distorting the member shape. The effect of welding on element strength is addressed in Section E.4.
E.6.1 Compression Members with Transverse Welds Transverse welds not at the ends of a column supported on both ends or in a cantilever column may appreciably decrease the member buckling strength. Sharp (1993) showed that for these cases the strength calculated as though the entire column were of welded material is conservative. If a column has both longitudinal and transverse welds, the strength determined considering the transverse welds usually is less than the strength determined considering the longitudinal welds. For circumferentially welded cylinders with Rb/t > 20, Sharp (1993) showed that Section B.5.4.5 may be very unconservative. Apparently the circumferential welds can cause more severe geometric imperfections in the thinwalled cylinder than those in relatively heavy-wall cylinders. More research is needed to establish accurate design rules for circumferentially welded, thin-walled cylinders.
E.6.2 Compression Members with Longitudinal Welds The strength of a cross section with only part of its area heat affected can be estimated by adding up the strength of the material in the heat-affected zone and the unaffected material outside this zone (Hill, et al. (1962)). Sharp (1993) showed that for calculating the member buckling strength, the buckling formula constants given in Table B.4.1 (non-artificially aged tempers) best represent weld-affected material.
January 2010
Chapter F Design of Members for Flexure F.1 General Provisions
F.2 Open Shapes
Resistance and safety factors are discussed in Sections B.3.2.1 and B.3.2.2.
F.2.1 Lateral-Torsional Buckling
F.1.1 Bending Coefficient Cb The bending coefficient is applied to segments of beams between brace points. Inflection points are not brace points. The lateral-torsional buckling strengths given in Sections F.2.1, F.3, F.4.2, and F.5 are based on a uniform moment over the unbraced length. If the moment varies over the unbraced length, the lateral-torsional buckling strength is greater than the strength given by Sections F.2.1, F.3, F.4.2, and F.5. This strength increase can be accounted for by using the bending coefficient Cb given in F.1.1 provided by Kirby and Nethercot (1979). F.1.1.1 Doubly Symmetric Shapes The formula for the bending coefficient is the same as used in the 2010 AISC Specification and given in the SSRC Guide 6th edition. If the free end of a cantilever is torsionally braced, equation F.1-1 can be used to compute Cb. The SSRC Guide 6th edition Section 5.2.9 provides additional information on cantilevers. F.1.1.2 Singly Symmetric Shapes Application of the Cb factor to singly symmetric sections in the same manner as for doubly symmetric sections has been shown to be unconservative in certain cases by Kitipornchai (1986). The unconservative cases arise if the Cb factor is applied to the critical moment determined for the case of larger flange in compression, ML, when it is possible that somewhere in the unbraced segment the smaller flange may be in compression. In such cases, the member must also be checked at the location where the smaller flange is subjected to its maximum compression. Kitipornchai (1986) showed that if one of the two flanges is small such that Icy/Iy ≤ 0.1 or Icy/Iy ≥ 0.9, Cb should be taken as 1.0. Cb is also to be taken as 1.0 if rotational restraint is considered (ky < 1) since Equation F.1-1 overestimates Cb when the unbraced length is factored by a ky less than 1. For continuous beams there are no directly derived values of C1 and C2. For this reason rational analysis must be used in estimating the values of these coefficients for such applications. It can be shown that for loading as shown in Figure CF.1.1, reasonably conservative results are obtained by taking: C1 = 0.41Cb and C2 = 0.47Cb when the smaller (top) flange is in compression (shown in the top two cases of Figure CF.1.1) and C1 = 0 and C2 = 0 when the larger (top) flange is in compression (shown in the bottom two cases of Figure CF.1.1). January 2010
In the inelastic stress range the lateral-torsional buckling strength equation employs the straight line approximation to the tangent modulus buckling curve that is also used for columns. Tests have shown this curve to be conservative for beams (Clark and Rolf (1966)). S1 isn’t needed for lateral-torsional buckling because yielding is addressed in Section F.8. Clark and Hill (1960) determined the lateral-torsional buckling strength of single web beams about their strong axis. A simple span beam restrained against movement laterally and vertically at the supports, but free to rotate about the vertical and horizontal axes at the ends is assumed. A symmetrical section and uniform moment are also assumed. The expressions Clark and Hill derived for lateral-torsional buckling were complicated, so a simplified approximate method for estimating strength was developed. An effective slenderness ratio L/1.2ry was found to be conservative for standard aluminum shapes. Section F.2.2 allows the designer to calculate a more accurate value for ry. The formulas of Section F.2.1 are based on an approximation in which the term Lb/ry replaces a more complicated expression involving several properties of the cross section. Because of this approximation, Section F.2.1 gives very conservative results for certain conditions, namely for values of Lb/ry exceeding about 50 and for beams with transverse loads applied in a direction away from the beam’s shear center. To compute more accurate bending strengths for these cases, the value of ry in Section F.2.1 may be replaced by the effective radius of gyration rye given in Section F.2.2. Figure CF.2.1 compares the slenderness ratios of 17 American Standard I-beams using ry and using rye. Using ry is very conservative for moderate and high slenderness ratios and for all of the sections, in many cases by a factor of two or more. Sharp’s (1993) comparison of test data and calculations using rye shows that using rye is conservative. For singly-symmetric sections unsymmetric about the bending axis Section F.2.2.2 or F.2.2.3 may be used. The latter is more accurate. Winter (1941) showed a method for taking advantage of the effect of bracing the tension flange. He derived the elastic critical moment Me for pure bending for a singly symmetric I-section with the tension flange prevented from lateral displacement but free to rotate:
EI c dπ2 GJ Me= _____ + ___ d Lb2
(CF.2-1)
rye can be evaluated for this case using this Me in Equation F.2-3. In equation CF.2-1 Ic is the moment of inertia of the compression flange about the web. II-25
Figure CF.1.1 ORIENTATION OF THE AXES AND CROSS-SECTIONAL NOTATION
F.2.2 Effective Radius of Gyration rye F.2.2.1 Shapes Symmetric About the Bending Axis Bending strengths are determined at the brace points of beams as well as between brace points. At brace points of doubly symmetric beams use Equation F.2-1 to calculate the allowable stress. Use the same equation between brace points if the beam is subjected to lateral loads that are applied only at the shear center of the section. Use Equation F.2-2 to calculate the allowable stress between brace points when a transverse load is applied to the top or bottom flange of the beam and the load is free to move laterally with the beam if it should buckle. Selection of the proper equation for rye is illustrated by Figure CF.2.2. At point B for both beams, use Equation F.2-1. Use the same equation for point A if the distributed load is applied at the level of the neutral axis. If the distributed load is not applied at the level of the neutral axis, use Equation F.2-2. The approach for checking the moment at II-26
point C is discussed in connection with the selection of Cb in Section F.2.2.3. F.2.2.2 Singly Symmetric Shapes Unsymmetric About the Bending Axis For singly symmetric shapes that are unsymmetrical about the bending axis, approximate bending strength can be determined using Section F.2.2.1 to determine rye taking ry, Iy, Sc and J as though both flanges were the same as the compression flange with the overall depth remaining the same. This approximation is quite conservative when the smaller flange is in compression. The approximation may be unconservative when the larger flange is in compression. F.2.2.3 Shapes Unsymmetric About the Bending Axis Section F.2.2.3 applies to shapes symmetric about the bending axis as well as shapes unsymmetric about the bending axis. However, Section F.2.2.1 gives the same results as January 2010
F.2.2.3 for shapes symmetric about the bending axis and is easier to apply. Therefore, to guide users to the most efficient way to use this Specification, the title for F.2.2.3 is “shapes unsymmetric about the bending axis”. Section F.2.2.3 applies to any beam bent about the strong axis by moments or by lateral loads applied through the shear center of the section. Equation F.2-4 was derived by Clark and Hill (1960) based on elastic torsional-flexural buckling theory. This expression considers non-symmetry of the section about the bending axis as well as the location of the laterally applied load with respect to the shear center. The orientation of the axes and the cross-sectional notation are illustrated in Figure CF.1.1. The magnitudes of yo, torsion constant J and the warping constant Cw can be determined from references such as Roark and Young (1989). The approximate formula for j given in Equation F.2-8 is based on work by Kitipornchai et al. (1986).
F.2.3 Interaction Between Local Buckling and Lateral-Torsional Buckling This Section accounts for the effect that the reduced stiffness due to local buckling may have on the lateral buckling strength of single web beams based on work by Sharp (1970). The nominal strength expression was rearranged from the expression given in the 2005 Aluminum Design Manual but gives the same strength.
F.3 Closed Shapes
Figure CF.2.1 EQUIVALENT SLENDERNESS RATIOS FOR LATERAL BUCKLING
This section applies to closed shapes, defined in the glossary as hollow shapes that resist lateral-torsional buckling primarily by torsional resistance rather than warping
Beam
A
A Moment diagram B
B
Beam C Moment diagram
Figure CF.2.2 BEAM AND MOMENT DIAGRAM EXAMPLES January 2010
II-27
resistance. The wall thickness need not be uniform. The_____ slenderness ratio of a closed shape used in Section F.3 L bS c is 1.6 _____ 2___ It was derived using the more general theoreti√I yJ cal equation for lateral buckling strength and ignoring the term that represents the warping resistance of the beam, since, for closed shapes, this term is usually small in comparison to the term that represents St. Venant torsion. The two terms are equal when Cw = 0.038JLb2. If Cw is not small compared to 0.038JLb2, Section F.2 gives more accurate results.
√
F.4 Rectangular Bars F.4.1 Yielding and Rupture Clark and Rolf (1966) showed that rectangular bars can undergo bending moments that are considerably greater than those predicted on the basis of the ordinary flexure formula and determined a shape factor for yielding of 1.30. Sharp (1993) determined shape factors for yielding of 1.32 and rupture of 1.46 for 6061-T6. This Specification uses 1.30 and 1.42, respectively.
F.4.2 Lateral-Torsional Buckling If a rectangular bar is laterally unsupported and is sufficiently narrow in cross section, it can fail by lateraltorsional buckling. Section ____ F.4.2 accounts for this limit state, using 2.3(d/t) √L b/d as the slenderness ratio. In the intermediate slenderness ratio range, the buckling strength is considerably affected by a redistribution of stress that accompanies plastic yielding, so that the apparent stresses at buckling are appreciably higher than values for single web beams. Clark and Rolf (1966) showed that the formula
for buckling strength agrees well with the results of tests on rectangular bars. The formulas are based on a uniform moment on a single span beam that is simply supported with the ends prevented from lateral deflection but free to rotate about the vertical axis.
F.5 Single Angles The strength of single angles in flexure in this Section is similar to the AISC Load and Resistance Factor Design Specification for Single-Angle Members, 2000. One difference from the AISC Specification for SingleAngle Members is that the yield strength is limited to 1.3My rather than 1.5My. This is done to be consistent with Sections F.8.1.2 and F.8.2.2. The local buckling strength of an angle leg depends on the degree of end fixity that the other leg provides and the variation in stress across the width of the angle leg. The lower bound on end fixity is a pinned support and the upper bound is a fixed support. Equivalent slenderness ratios (from Sharp (1993) Table 7.1) are summarized in Table CF.5.1 for an angle leg of width b and thickness t. Case 1, uniform compression in an angle leg, is addressed in Section F.5a(2). Cases 2, 3, and 4 are addressed in Section F.5a(1) by conservatively using the worst case (Case 2) and assuming that the support is restrained slightly more than the pinned condition so that a factor of 4 (vs. 4.45) can be used.
F.5.1 Bending About Geometric Axes Bending about geometric axes occurs when the moment is applied about an axis parallel to a leg of the angle as shown in Figure F.5.4. In such cases, when an angle is lat-
Table CF.5.1 EQUIVALENT SLENDERNESS RATIOS FOR ANGLE LEGS Case
Stress distribution on leg of angle
Equivalent slenderness ratio/(b/t) (pinned support)
Equivalent slenderness ratio/(b/t) (fixed support)
5.13
2.89
4.45
2.62
3.64
2.27
2.56
1.36
Angle orientation
free edge 1 supported edge free edge 2 supported edge free edge 3 supported edge free edge 4 supported edge
II-28
January 2010
erally restrained at the point under consideration, the neutral axis is the geometric axis as shown on the left side of Figure F.5.4 and addressed in subsections a and b. When the angle is laterally unrestrained, the section will deflect laterally as well as normal to the bending axis, causing the neutral axis to incline as shown on the right side of Figure F.5.4 and addressed in subsection c.
F.5.2 Bending About Principal Axes Formulas for determining bw are given in Part V. Since these formulas are cumbersome, bw values for some common angle sizes are given in Table CF.5.2. bw varies only slightly with angle thickness for the angles listed in ADM Part V.
Table CF.5.2 Angle Size (in.)
ßw (in.)
8×6
3.31
8×4
5.48
7×4
4.37
6×4
3.14
6 × 3.5
3.69
5 × 3.5
2.40
5×3
2.99
4 × 3.5
0.87
4×3
1.65
3.5 × 3
0.87
3.5 × 2.5
1.62
3 × 2.5
0.86
3×2
1.56
2.5 × 2
0.85
equal legs
F.6.2 Local Buckling The inelastic buckling strength of round tubes in bending is based on experimental work by Clark and Rolf (1964). S2 is the slenderness Rb/t at which the bending buckling strength and axial compression buckling strength curves intersect. For values of Rb/t greater than S2, the bending buckling strength is conservatively assumed to be the same as the axial compression buckling strength. This is shown in Figure CF.6.1 for 6061-T6. The lower set of lines, two straight lines and a curved line, applies to both tubes and curved elements under uniform compression. The upper set of lines, three straight lines and one curved line, applies to tubes in flexure. The higher strengths at low R/t ratios reflect the additional strength due to the shape factor on bending for a tube (1.17). For larger R/t ratios the strength equations for axial compression also apply to bending members. For curved elements in bending members, experience with building sheathing products shows that their strength is lower than that for complete cylinders for low R/t ratios, and thus the dashed line on Figure CF.6.1 is used for this case. The limitation of applicability of this Section to Rb/t ≤ 20 for tubes with circumferential welds is the same as that of Section E.6.1.
F.7 Rods The shape factors used for yielding and rupture of 1.30 and 1.42, respectively, are conservatively taken as the same as those for rectangular bars.
0.00
bw is positive or negative depending on the direction of bending.
F.6 Pipes and Round Tubes F.6.1 Yielding and Rupture Clark and Rolf (1964) demonstrated that yielding of round hollow beams does not occur until the bending moment considerably exceeds the yield moment predicted by the ordinary flexure formula. This results from the non-linear distribution of stress in the inelastic range. Yielding does not become apparent as soon as the calculated stress in the extreme fiber reaches the yield strength because the less highly stressed fibers near the center of the beam are still in the elastic range. The constants 1.17 and 1.24 used in the yielding and rupture strengths can be considered as shape factors for yielding and ultimate strength, respectively. The factor on yield was picked from curves of yield strengths at 0.2 percent offset for tubes with proportions similar to those listed in ADM Part V. The shape factor on ultimate strength was deduced from apparent and actual stress-strain curves at a stress corresponding to tensile rupture strength of the material. January 2010
Figure CF.6.1 TUBES AND CURVED ELEMENTS IN COMPRESSION OR BENDING II-29
F.8 Elements of Flexural Members F.8.1 Tension F.8.1.1 Elements in Uniform Tension The strength of elements in uniform tension is the same as the strength of members in axial tension addressed in Section D.2. F.8.1.2 Elements in Flexure The shape factors for flat elements in flexure are the same as the shape factors for solid rectangular shapes in F.4.1. Shape factors for aluminum are less than those for the rigidplastic cases commonly used for mild steel because of the rounded stress-strain curves for aluminum alloys. The effect of alloy on shape factor is not very large, so only one set of shape factors is given. Sharp (1973) tested beams with longitudinal and transverse welds in tension.
F.8.2 Compression See Section E.4 for a discussion of the strength of longitudinally-welded elements. F.8.2.1 Elements in Uniform Compression The strength of beam elements in uniform compression is the same as the strength of column elements in uniform compression. These are given in Section B.5.4.
F.8.2.3 Alternate Compressive Flexural Strength See the commentary to Sections B.5.4.6 and B.5.5.4.
F.8.3 Weighted Average Flexural Strength Tests by Jombock and Clark (1968) of formed sheet beams were the basis for the weighted average compression and tensile bending strengths in Specification editions prior to 2005. Kim (2003) improved the weighted average method accuracy for a variety of members. The distance c for a tensile flange is the distance to its extreme fiber because tension fracture initiates there. The distance c for a compression flange is the distance to its centerline because buckling is based on the flange’s average stress.
F.9 Welded Flexural Members F.9.1 Flexural Members with Transverse Welds For tubes with circumferential welds, Section F.8.2.1.6 only applies if Rb/t ≤ 20. If Rb/t > 20, Section F.8.2 is unconservative.
F.9.2 Flexural Members with Longitudinal Welds The lateral-torsional buckling strength of flexural members with longitudinal welds is taken as a weighted average of the welded and unwelded strengths.
F.8.2.2 Elements in Flexure The shape factors for flat elements in flexure are the same as the shape factors for solid rectangular shapes in F.4.1. Additionally, for flexural compression, buckling is addressed in Section B.5.5.
II-30
January 2010
Chapter G Design of Members for Shear G.1 General Provisions The shear strength is limited only by the shear yield strength Fsy, and not the shear ultimate strength Fsu. This simplification is used because for the alloy/temper products in this Specification, the shear ultimate strength divided by the ultimate safety factor (1.95) is at least 90% of the shear yield strength divided by the yield safety factor (1.65). Similarly, the shear ultimate strength multiplied by the ultimate resistance factor (0.75) is at least 90% of the shear yield strength multiplied by the yield resistance factor (0.90). The strength of welded webs is based on shear fracture in the weld-affected area and the weighted average shear strength of the welded and unwelded zones. The shear ultimate strength is divided by 1.2 to provide a safety factor of 1.95 (= 1.2 × 1.65) or a resistance factor of 0.75 (= 0.90/1.2) once Fs has been factored by the safety and resistance factors given in Section G.1. Shear yielding in the weld-affected area is not considered to be a limit state, since the maximum shear stress would have to occur over a long enough length of the member to cause excessive deflection, and this is rare.
G.2 Members with Flat Webs Supported on Both Edges The buckling strength of unstiffened flat webs is for a web with partial restraint against rotation at the attachment to the flanges. The corresponding value of the slenderness ratio is 1.25b/t based on Bleich (1952) and Gerard and Becker (1957). The buckling strength in the inelastic range was developed originally for shear buckling of tubes (Clark and Rolf (1964)) but also applies to flat elements in shear. For webs with transverse stiffeners, the web’s edges are assumed to be partially restrained against rotation, giving an equivalent slenderness ratio of
January 2010
1.25a 1 ________ _________ a 12 t√1+0.7( a__ 2 )
A stiffened flat web that has buckled in shear can continue to carry load by diagonal tension action in the web (Moore (1947)), but this is not accounted for in the provisions of Section G.2. The required moment of inertia for the transverse stiffener is sufficient to limit local buckling of shear webs to the panels between stiffeners and to provide postbuckling strength in the web. This moment of inertia is multiplied by the ratio of the applied shear load to the shear load causing buckling to adjust the stiffener size for the actual load applied. These formulas were used in the specifications published by ASCE ( 1962a, 1962b), agree well with the results of tests by Moore (1942) and are conservative in comparison with the stiffener size theoretically derived by Cook and Rockey (1962). Hartmann and Clark (1963) and Sharp and Clark (1970) provide further background.
G.3 Round or Oval Tubes The provisions for transverse shear of round or oval tubes are based on local buckling of cylinders subjected to torsion, which is addressed in Section H.2.1. Since torsion is usually constant along the cylinder length but transverse shear usually varies along the length, the transverse shear strength is taken as 1.3 times the torsion strength as suggested by Galambos (1998) in Section 14.3.4. This treatment is similar to AISC (2005). In equation G.3-1, Vn = Fs Ag/2, it is assumed that the shear stress at the neutral axis VQ/(Ib) = Fs. For thin round tubes of radius R and thickness t, I = pR3t, Q = 2R2t, and b = 2t, which gives the shear stress at the neutral axis as V/(pRt) = V/(Ag/2).
II-31
Chapter H Design of Members for Combined Forces and Torsion H.1 Members Subject to Flexure and Axial Force Use of the interaction equation given in H.1 is predicated on a stability analysis performed in accordance with Chapter C. If the analysis is not performed in accordance with Chapter C, using the interaction equation given in Section H.1 can be unconservative.
H.2 Members Subject to Torsion H.2.1 Round or Oval Tubes The equation for equivalent h/t is based on the theoretical elastic buckling strength of cylinders in torsion. Tubes loaded in torsion are not as sensitive to the effect of initial imperfections in the geometry as are tubes loaded in axial compression. Battdorf, et. al. (1947) showed this gives good agreement with the results of tests on thin cylinders that fail in the elastic range, and Clark and Rolf (1964) showed this agrees well with experimental results in the inelastic stress range. The elastic buckling strength of cylinders in torsion matches AISC (2005) Specification Section H.3.1, since
Figure CH.2.1 SHEAR BUCKLING OF TUBES WITH CIRCUMFERENTIAL STIFFENERS
π E 1.23E ____ (_______ = __________ 5/4 1.25λt )2 √ L/D (D/t) 2
where λt = 2.9(R/t)5/8(L/R)1/4 and R = D/2 Sharp (1993) noted that the equivalent slenderness ratio for tubes can give very conservative results for long tubes with both longitudinal and circumferential stiffeners. Figure CH.2.1 shows the change in the coefficient in Equation H.2-2 with length of tube. A coefficient of 2.9 is specified for all cases (solid line in Figure CH.2.1). A more accurate and less conservative value for long tubes is less than 2.9 as illustrated by the dashed line in Figure CH.2.1. The ordinate in this figure is a rearrangement of Equation H.2-2. The addition of longitudinal stiffeners as well as circumferential stiffeners usually increases the shear strength of a tube compared to a tube with circumferential stiffeners only.
H.2.2 Rectangular Tubes Rectangular tubes were not specifically addressed before the 2010 Specification. The 2005 AISC Specification section H3.1(b) addresses rectangular tubes with equations that give the same limit state shear stress as the equations given in AISC Specification section G2.1(b)(i). H.2.2 matches the AISC approach, but uses the limit state shear stresses for aluminum webs given in the 2010 SAS Section G.2.1. The torsion constant C for rectangular tubes of constant wall thickness t may be conservatively taken as
II-32
C = 2(b - t)(d - t)t - 4.5(4 - π)t3 where b = width of the tube d = depth of the tube.
H.2.3 Rods Since shear buckling cannot occur in a rod, Section H.2.3 simply uses shear yielding as the limit state shear stress for a rod.
H.3 Members Subject to Torsion, Flexure, Shear, and/or Axial Compression H.3.1 Flat Elements Equations H.3-1 and H.3-2 are documented in Galambos (1998) (equation 4.32).
H.3.2 Curved Elements Equations H.3-3 and H.3-4 are documented in Galambos (1998) (equation 14.57), which is based on work by Schilling (1965).
January 2010
Chapter J Design of Connections J.1 General Provisions The maximum fastener spacing for tension member components are based on experience rather than tests or theory. Limiting the fastener spacing for tension member components reduces the chance of buckling if unanticipated compression acts on the member. The maximum fastener spacing in built-up compression members is based on preventing buckling of the components between points of attachment.
attaching bearing stiffeners. Examples of longitudinally loaded fillet welds that are not end-loaded include: a) welds that connect parts to form built-up members in which shear is applied to each incremental length of weld depending on the shear distribution along the member’s length; b) welds attaching beam web connection angles and shear plates, because the flow of shear from the beam web to the weld is nearly uniform along the weld’s length; and c) welds attaching stiffeners to webs, since the stiffeners and welds are not subject to calculated axial stress and only serve to keep the web flat.
J.2 Welds
J.2.2.2 Strength
Aluminum welded connection types include groove welds, fillet welds, plug and slot welds, and stud welds. Moore et al. (1971) and Sharp et al. (1982) documented strengths of aluminum welded connections.
Menzemer and Iasconne (2002) established the shear strengths of fillers 4047, 4643, and 5183. Nelson and Rolf (1966) established the shear strengths of the other fillers. They used the same test method to determine shear strength. Allowable stresses for fillet welds for various combinations of base metals are given in Part VI, Table 6-2, and LRFD design stresses are given in Part VI, Table 6-4. The strength of a fillet weld is usually governed by the strength of the filler metal rather than the base metal.
J.1.3 Maximum Spacing of Fasteners
J.2.1 Groove Welds J.2.1.1 Complete and Partial Penetration Groove Welds Groove welds are classified as either complete penetration or partial penetration for the purpose of determining the weld size. The method of classifying a groove weld is the same as that in AWS D1.2. Groove welds made with permanent backing have less fatigue strength than groove welds without permanent backing. J.2.1.2 Effective Area The definition of effective area matches that given in AWS D1.2. J.2.1.3 Strength Allowable stresses for groove welds for various combinations of base metals are given in Part VI, Table 6-1, and LRFD design stresses are given in Part VI, Table 6-3. The strength of a groove weld is usually governed by the strength of the base metal rather than the filler metal.
J.2.2 Fillet Welds J.2.2.1 Effective Throat and Effective Length The effective throat and effective length definitions match those in AWS D1.2-2008. Boxing is defined by AWS A3.0 as “the continuation of a fillet weld around a corner of a member as an extension of the principal weld.” The effective throat of an equal leg fillet weld of size S is 0.707Sw. End-loaded fillet welds are oriented parallel to the stress in the member and transmit load to the end of an axially loaded member. Examples include longitudinally welded lap joints at the ends of axially loaded members and welds January 2010
J.2.3 Plug and Slot Welds Plug and slot welds are primarily used to transmit shear in the plane of the weld. An example is a cover plate attached to a flange with plug welds. The definition of effective area and the limit on slot length match those in AWS D1.2 Section 2.5.
J.2.4 Stud Welds Table J.2.2 and Table J.2.2M match AWS D1.2. The base metal thickness provisions match those in AWS D1.2 Sections 6.9.3 and 6.13.5.
J.2.5 Post-Weld Heat Treating The strengths for 6005 and 6063 lighting pole assemblies artificially aged after welding are based on a report by the Texas Transportation Institute (1980).
J.3 Bolts J.3.1 Bolt Material a) ASTM F468, Nonferrous Bolts, Hex Cap Screws, and Studs for General Use, includes 2024-T4, 6061-T6, and 7075-T73 aluminum bolts and provides the strengths that are used in Table A.3.8. Bolt dimensions are given in Part VI, Table 5-4. ASTM F467, Nonferrous Nuts for General Use, includes 2024-T4, 6061-T6, and 6262-T9 aluminum nuts. Nut dimensions are given in Part VI, Table 5-5. II-33
b) The AISC Specification for Structural Steel Buildings includes design rules for ASTM A307, A325, and A449 steel bolts. The Rockwell C35 hardness limit is intended to avoid hydrogen-assisted stress corrosion cracking of the bolt (see Section J.5.1 commentary). The zinc coating options match ASTM steel bolt specs A307, A325, A354, and A449, which specify that zinc coating be either hot-dip per A153 or mechanically deposited per B695. c) ASCE 8-02, Specification for the Design of ColdFormed Stainless Steel Structural Members, provides design rules for fasteners meeting ASTM F593, Stainless Steel Bolts, Hex Cap Screws, and Studs.
J.3.2 Holes and Slots for Bolts It may be appropriate to limit hole diameter to 1/32 in. larger than the bolt diameter for bolts with a nominal diameter of 3/8 in. or less.
J.3.3 Minimum Spacing of Bolts The minimum spacing requirement is intended to provide sufficient clearance for installation tools and washers.
J.3.4 Minimum Edge Distance of Bolts Edge distance requirements (2D for full bearing strength and a minimum of 1.5D with reduced bearing strength) have been selected so that for a single fastener, the block shear strength equals or exceeds the bearing strength. So for a single fastener, meeting the bearing requirements negates the need to check block shear. Edge distance requirements apply to free edges of a part only, and not to the corner of a structural shape such as the heel of an angle.
J.3.5 Bolt Tension The use of the root area for determining the tensile strength of aluminum fasteners rather than the slightly larger tensile stress area used for steel fasteners is based on Dewalt and Mack (1980). The root area is based on the nominal minor diameter of external threads (D - 1.191/n) given in ASME B1.1-1989, Unified Inch Screw Threads (reaffirmed in 2001) section 10.1. Part VI, Table 5-3 gives tensile strengths for 2024-T4 and 7075-T73 bolts and cap screws. The safety factor for bolt shear, bolt tension and rivet shear (2.34) is higher than for members (1.95) because it is preferable for the connections to be stronger than the members. If connections have greater strength, it is more likely that the structure will exhibit warning of an overload (e.g., excessive deflection and/or yielding of the members). Another reason for this higher safety factor is to lessen the likelihood that connection capacity-reducing conditions (e.g., limited amounts of corrosion or improper installation of fasteners) will have an adverse effect on the member’s II-34
ability to reach its calculated nominal strength. Improper installation may include over- or under-tightening, missing nuts or washers, or presence of threads in the shear plane when this was not the design condition.
J.3.6 Bolt Shear Rather than using approximate relationships between the threaded and unthreaded areas of bolts and different design stresses when threads are in the shear plane and when threads are not in the shear plane, this Specification uses the same design stress for both cases and adjusts the effective shear area appropriately. Part VI, Table 5-3 gives shear strengths for 2024-T4 and 7075-T73 bolts and cap screws with threads in and threads not in the shear plane. The root area term in equation J.3-2 matches the formula given in ASME B1.1 (1989).
J.3.7 Bolt Bearing The limit state of bearing is reached when elongation of the fastener hole becomes excessive. Menzemer et al. (2001) established the bearing strength as 2Ftu for a load at which hole deformation is approximately D/4, where D is the nominal diameter of the bolt. Sharp (1993) and the Department of Defense (1994) show that for ratios of edge distance to fastener diameter as small as 1.5, it is conservative to reduce the allowable bearing stress by the ratio of the edge distance to twice the fastener diameter. Moisseiff et al. (1944) demonstrated that a relatively even distribution of load among the fasteners is achieved before ultimate failure of mechanically fastened joints in structural aluminum alloys. For countersunk holes, caution should be exercised when the depth of the countersink approaches the thickness of the part, creating a knife-edge on the hole which may be easily damaged.
J.3.8 Slip-Critical Bolted Connections J.3.8.1 General This Section is based on European specifications and testing conducted by Kissell and Ferry (1997). Aluminum slip-critical connections are included in Canadian, British, ISO, and Eurocode specifications. In the US, use of high strength steel bolts is governed by the Research Council on Structural Connections (RCSC) Specification for Structural Joints Using ASTM A325 or A490 Bolts. The RCSC Specification addresses the use of these high strength steel bolts to connect steel parts and so is modified here for connections using aluminum parts. All parts of the RCSC Specification not modified by the provisions of Section J.3.8 (for example, provisions on inspection) apply to aluminum slip-critical connections. Slip-critical connections resist shear by friction between the faying surfaces of the connected parts, which are tightly January 2010
clamped together by high strength steel bolts. Slip-critical connections are used when it is desirable to prevent movement of connected parts relative to one another. Such connections are useful for joints subjected to dynamic or fatigue loads, as well as joints in which both bolts and welds share the load, joints with oversize holes, and joints with slotted holes with loads not applied normal to the axis of the slot. In addition to the requirements for bearing connections, slip-critical connections are subject to the additional requirement that the slip resistance of the joint be greater than the applied shear loads. The design strength of slipcritical connections cannot be greater than the design strength of the same connection designed as a bearing connection. The design strength of a slip-critical connection is limited to the lesser of the design strength of the bolt in shear and bearing and the slip resistance of the joint.
and nuts galvanized by different processes may result in an unworkable assembly. J.3.8.3 Holes For convenience, nominal hole dimensions from the RCSC Specification are given in the Table CJ.3.1. J.3.8.4 Design for Strength Slip-critical connections must be designed assuming slip could occur, placing shear on the bolt and bearing on the sides of the hole. Bolt shear strengths are the same as in the RCSC Specification. Bolt design shear strengths should be reduced appropriately in long connections since bolts at the end of such connections bear a higher shear force than bolts near the middle of the length of these connections. (The RCSC Specification requires shear strengths be reduced by 20% in connections whose length between extreme fasteners measured parallel to the line of force exceeds 50 in. (1300 mm)).
J.3.8.2 Material Since hot-dip galvanizing may embrittle A490 bolts and galvanizing is required to discourage galvanic corrosion between the steel fastener and the aluminum parts, A490 bolts are not allowed in aluminum slip-critical connections. The RCSC Specification limits the bearing stress under the bolt head in steel to 64 ksi for steel with a yield strength less than 40 ksi by requiring such steel with A490 bolts to have washers. The Specification for Aluminum Structures requires the use of washers under bolt heads and nuts, and bearing stresses under the washer can reach approximately 24 ksi (165 MPa) with A325 bolts. Therefore, aluminum slip-critical connections are limited to those alloys with a tensile yield strength of 15 ksi (105 MPa) or greater. Thin parts, such as aluminum sheet and drawn tube, are effectively prohibited from slip-critical connections by bearing stress limitations on the sides of the hole. ASTM A325 allows both hot-dip galvanizing and mechanical galvanizing of fasteners. A325 further requires that all components of a fastener assembly (bolt, nut, and washer) be coated by the same process, since mixing bolts
J.3.8.5 Design for Slip Resistance Slip coefficients are given for two contact surfaces: roughened aluminum on roughened aluminum, and roughened aluminum on zinc-rich painted steel. Kissell and Ferry (1997) tested these surfaces in accordance with the test method given in the RCSC Specification for both slip and creep. Slip coefficients for other surfaces may be determined by testing in accordance with the RCSC Specification. Luttrell (1999) and Fortlin, et al. (2001) showed that bolt tension is not significantly affected if the temperature changes from the installation temperature. Tests of mill finish aluminum surfaces degreased and dried have generally achieved relatively low coefficients of friction. J.3.8.6 Washers Washers are required under all bolt heads and nuts. This requirement is intended to minimize galling of the outer ply of aluminum and creep relaxation of bolt tension.
Table CJ.3.1 HOLE DIMENSIONS FOR SLIP-CRITICAL JOINTS Hole Dimensions (in.) Bolt Diameter (in.)
Standard (Diameter)
½
9
⁄8
11
5
Oversized (Diameter)
Short Slotted (Width × Length) ⁄16 × 11⁄16
9
⁄16 × ⁄8
11
⁄16
5
⁄8
9
⁄16
13
⁄16
11
⁄16
15
⁄16
¾
13
⁄8
15
7
13
⁄16 × 1 7⁄8
⁄16 × 1 ⁄8
1
1 1⁄16
1¼
1 1⁄16 × 1 5⁄16
≥1 ⁄8
d + ⁄16
d + ⁄16
(d + ⁄16) × (d + ⁄8)
1
January 2010
1
5
15
1
⁄16 × 1 9⁄16
15
1 ⁄16 1
⁄16 × 1 ¼
⁄16 × 1
13
⁄16
7
Long Slotted (Width × Length)
1
⁄16 × 2 3⁄16
1 1⁄16 × 2 ½ 3
(d + 1⁄16) × (2.5d)
II-35
J.3.9 Lockbolts
ASTM B 316, Aluminum and Aluminum-Alloy Rivet and Cold-Heading Wire and Rods, provides the strengths that are used in Table A.3.9.
Screw connection tests used to formulate the provisions included single fastener specimens as well as multiple fastener specimens. However, it is recommended that at least two screws should be used to connect individual elements. This provides redundancy against under torquing, over torquing, etc., and limits lap shear connection distortion of flat unformed members such as straps. The safety factor for screwed connections in buildingtype structures is 3.0, which matches AISI (2001). The safety factor for screwed connections in bridge structures is 3.0(2.20/1.95) = 3.38, rounded to 3.5. The safety factor for screw bearing is consistent with the safety factor for screw shear and tension.
J.4.2 Holes for Cold-Driven Rivets
J.5.1 Screw Material
Holes for cold-driven rivets are sized so that the rivet completely fills the hole when driven.
The material for screws used to connect aluminum parts is selected to meet strength and corrosion resistance considerations. Steel screws with a Rockwell hardness of C35 or greater may suffer hydrogen-assisted stress corrosion cracking (HASCC) where exposed to certain dissimilar metals, moisture, and tensile stress due to installation or loading. For this reason, steel screws with a Rockwell hardness of C35 or greater are not permitted. Aluminum and austenitic stainless steel screws do not experience HASCC. When fasteners will not be exposed to contact with liquid water or humidity near the dew point, certain other steels, with appropriate hardness, and appropriately coated and/ or plated are also acceptable. An example is 430 stainless steel, which has a nominal composition of 16% chromium.
A lockbolt assembly includes a pin, which is similar to a bolt, and a collar, which performs the function of a nut. The collar is swaged onto locking grooves on the pin. Lockbolts are available in carbon steel, stainless steel, and aluminum.
J.4 Rivets J.4.1 Rivet Material
J.4.4 Minimum Edge Distance of Rivets See Section J.3.4.
J.4.5 Rivet Tension Rivets are sensitive to grip (the thickness of the parts joined) and hole size, since these parameters affect the fastener’s head dimensions, unlike bolted installations. If the hole is too large or mislocated, or if the parts are slightly thicker or thinner than the thickness the rivet was selected for, the rivet head formed during installation is imperfect. These effects are greater on tensile strength than shear strength, since unless the rivet falls out of the connection, shear can still be resisted, but in tension the parts can begin to disengage without a proper head on both sides of the parts joined. The tensile strength of riveted connections, therefore, can vary significantly.
J.4.6 Rivet Shear The shear strength of aluminum rivets is based on the rivet filling the hole so the effective shear area of the rivet is the nominal hole diameter.
J.4.8 Blind Rivets Installing blind rivets requires access to only one side of a connection.
J.5 Tapping Screws Screwed connection provisions are based on Peköz (1990), who considered over 3500 tests on light-gage steel and aluminum connections worldwide. ECCS (1987) and BSI (1987) were also considered. Proper installation of screws is important to achieve satisfactory performance. Power tools with adjustable torque controls and driving depth limitations are usually used. II-36
J.5.2 Holes for Screws This Specification requires that the nominal diameter of unthreaded holes for screws shall not exceed the nominal diameter of the screw by more than 1/16 in. (1.6 mm). Many designers specify that the nominal diameter of unthreaded holes for screws shall not exceed the nominal diameter of the screw by more than 1/32 in. (0.8 mm). Table J.5.1 is based on AAMA (1991) Table 20, which was used for the hole sizes used for the pull-out testing that Section J.5.5.1.1 pull-out strengths are based on. Table J.5.2 is based on AAMA (1991) Table 21, which was used for the hole sizes used for the pull-out testing on which Section J.5.5.1.1 pull-out strengths are based.
J.5.3 Minimum Spacing of Screws See Section J.3.3.
J.5.4 Minimum Edge Distance of Screws See Section J.3.4.
J.5.5 Screwed Connection Tension The smallest screw head or washer size allowed is 5/16” since the diameter of a hex washer head for a No. 8 screw (the smallest screw size allowed by this Specification) is 5/16”. January 2010
J.5.5.1 Pull-Out J.5.5.1.1 Screws in Holes
The equations for pull-out are derived from research conducted by AAMA (2000), including over 400 pull-out tests. These equations are based on three regions of behavior: yield (circumferential stretching and bending of the aluminum around the screw), shearing of the internal threads in the hole, and a transition region between yield and shearing. For most cases they are less conservative than the pull-out equation in the Specification’s 6th edition (Pnot = 0.85tc DFtu2), especially for UNC threads in aluminum parts thicker than 0.084 in. (2.1 mm). Pull-out strengths are a function of the type of thread: coarse (UNC) or spaced. A UNC thread is often referred to as a “machine” thread, and a spaced thread screw is termed a “sheet metal” screw. Internal thread stripping areas Asn are given in Part VI Table 5-6 for Class 2B UNC threads. J.5.5.1.2 Screws in Screw Slots
Menzemer (2008) tested spaced thread screw types and machine thread screw types to develop Equation J.5-7. The average of all spaced thread tests was 0.2% greater than the strength given by Equation J.5-7, and the average of all machine thread tests was 4.2% greater than the strength given by Equation J.5-7. Because both spaced threads and machine thread pull-out strengths matched Equation J.5-7 well, this Specification does not provide different strengths for the different screw types. J.5.5.2 Pull-Over Sharp (1993) provided the pull-over strength equation for non-countersunk screws. Screws may be placed through the valley or the crown of corrugated roofing and siding. (See Figure CJ.5.1). A coefficient of 0.7 is used when the connected parts are not in contact, such as for fastening through the crown of roofing when a spacer block is not used between the roofing and the structural member supporting the roofing. The test strengths of such screwed con-
nections are more variable than those with the connected parts in direct contact at the connection such as the fastener through the valley in Figure CJ.5.1. Alternate pull-over strengths are given for screws in tight-fitting holes based on tests conducted by LaBelle and Dolby (2009). In these tests, screws had hex heads with integral washers. Screw nominal diameters were 0.164, 0.190, 0.216, and 0.25”, and part nominal thicknesses were 0.04, 0.06, 0.09, and 0.125”. The holes were “free fit” with the following nominal sizes: Screw Size
Hole Diameter (in.)
Drill Size
8
0.177
16
10
0.201
7
12
0.228
1
¼
0.266
H
These hole sizes average 0.013” larger than the screw diameter, smaller than the 0.062” oversize the Specification for Aluminum Structures allows. The average ratio of predicted strength (using Specification equation J.5-9) to test strength was 0.83 with a coefficient of variation of 7.3%. The equation for the pull-over strength of countersunk screws is based on over 200 tests by LaBelle and Dolby (2004) using 5 different flathead screw sizes, 6 sheet thicknesses, and 2 alloy-tempers. Testing was limited to commonly used screws with 82 degree nominal angle heads, so the equation is not known to apply to other head angles. Variation in actual diameters of hand-drilled countersunk holes can have a significant effect on pull-over strength. Caution should be used to avoid excessive oversizing of countersunk holes. Oversizing should be limited so that the top of the screw head is no more than the lesser of t1/4 and 1/32 in. (0.8 mm) below the top of the sheet. J.5.5.3 Screw Tension The tensile strength of aluminum screws is given in Part VI Tables 5-1 and 5-2.
Figure CJ.5.1 FASTENERS IN ROOFING January 2010
II-37
J.5.6 Screwed Connection Shear Screwed connections loaded in shear have limit states of screw shear, block shear rupture (see Section J.6.3), tilting, and bearing failure of the joined materials. J.5.6.1 Screw Bearing Based on limited testing, it appears that the bearing force exerted on a connected part by a screw should be limited to that which produces a hole elongation of D/8 to avoid threads disengaging from the sides of the hole. Therefore, testing is recommended to establish the bearing strength of screwed connections that are subjected to both bearing and tensile loads. J.5.6.2 Screw Tilting Screw tilting occurs when the part under the screw head is thicker than the part beneath it. The shear force on the joint causes the axis of the screw to tilt toward the plane of the connected parts and the screw threads to tear out of the lower sheet.
Specification for Structural Steel Buildings 1993 edition, Section J4.3. Marsh (1979) also studied this issue.
J.7 Bearing Strength of Flat Surfaces and Pins The bearing strength for flat surfaces and elements with pins in holes is 2/3 the bearing strength for elements with fasteners in holes. This is because bearing on flat surfaces and on elements with pins can tolerate less deformation than a fastener in a hole at the bearing limit state.
J.8 Flanges and Webs with Concentrated Forces J.8.1 Crippling of Flat Webs The formulas given in this Section are based on Sharp (1993). The crippling strength is a post-buckling strength.
J.8.2 Bearing Stiffeners
The shear strength of aluminum screws is given in Part VI Tables 5-1 and 5-2.
This Specification addresses bearing stiffener size by requiring that the stiffener be sized for the bearing load as a member in axial compression. If the stiffener is also being used as a shear stiffener, it must also meet the requirements of Section G.2.2.
J.6 Affected Elements of Members and Connectors
J.8.3 Combined Crippling and Bending of Flat Webs
J.6.2 Strength of Connectors in Shear
The formulas given in this Section are empirical, based on Sharp (1993).
J.5.6.3 Screw Shear
The resistance factor for shear yielding of connectors (1.00) is higher and the safety factor (1.50) is lower than for shear yielding of members. This is because shear yielding of connectors is unlikely to produce significant deformation of the structure as a relatively small portion of the structure is comprised of connectors.
J.6.3 Block Shear Strength The block shear rupture strength is based on work by Menzemer (1999) and is the same as in the AISC LRFD
II-38
J.9 Roofing and Siding Connections J.9.3 Fasteners in Laps The minimum size of #12 screws or 3/16 in. (5 mm) diameter rivets is specified in end laps and side laps to give neat, weather-resistant closures. In many cases, the primary, sheet-to-support fasteners will give satisfactory closures at the endlaps, but in side laps additional fasteners should be used if the joint does not interlock.
January 2010
Chapter L Design for Serviceability L.1 General Provisions This chapter addresses preserving a structure’s appearance, maintainability, durability, occupants’ comfort, or function. Specific limits on parameters (for example, deflection) are not provided, since these depend on the type of structure and its use.
L.2 Camber Camber should be measured without load acting in the camber plane. This may be achieved by measuring camber with a beam resting on a flat surface parallel to the camber plane.
L.3 Deflections Members and structures deflect under load. For example, the lateral deflection of a building under wind load is called drift. If the compressive stress exceeds the elastic local buckling stress Fcr, the full section is not effective in resisting deflection. This Specification only allows this if the element strength is based on post-buckling strength as it is in Sections B.5.4.1, B.5.4.2, B.5.4.3, B.5.5.1, and B.5.5.3. Reduced effective section provisions do not apply to B.5.4.4, for example, since this section does not allow post-buckling strength for such elements (supported on both edges and with an intermediate stiffener). The method used to account for the effect of local buckling on the post-buckling behavior of structural members is to consider that at stresses above the local buckling stress only part of the buckled element is effective in carrying load. Sooi and Peköz (1993) and Jombock and Clark (1968) documented this approach. AAMA TIR A11 limits deflections of components that support glass or similar brittle materials. Some building codes also limit deflections.
L.4 Vibration Vibration of aluminum structural members can cause fatigue failures. Vibrations may be caused by cyclically
January 2010
applied loads from machinery, by wind or other fluids moving over the structure, or by traffic on a bridge. When the frequency of the applied load is close to the natural frequency of the structure, the amplitude of the vibrations can be large, especially for lightly damped structures. The amplitude of the vibrations can be minimized by adjusting the stiffness of the structural components so that the natural frequency of the structure is less than half or more than twice the frequency of the applied loads or by sufficiently dampening the structural movement.
L.5 Wind-Induced Motion Wind on round tube members can cause motion of the members due to vortex shedding, by which regular impulses transverse to the wind direction are caused by the shedding of vortices on alternating sides of the member. Sharp (1993) gives the frequency of vortex shedding as f = SV/d where
f = vortex shedding frequency V = wind velocity d = outside diameter of tube S = Strouhal number = 0.2 for tubes.
If this frequency is near the natural frequency of the tube and sufficient damping is not provided, wind-induced motion will be large. (See Section L.4).
L.6 Expansion and Contraction Aluminum’s coefficient of thermal expansion is approximately 13 × 10-6/°F (23 × 10-6/°C). For structures exposed to ambient temperature fluctuations, provision for thermal movement such as expansion joints may be required to limit stresses.
L.7 Connection Slip Slip-critical connections are addressed in Section J.3.8.
II-39
Chapter M Fabrication and Erection M.1 Layout
M.5 Bending
M.1.1 Punch and Scribe Marks Hole centers are commonly located by punching, and cutoff lines are often scribed. Center punching and scribing should be avoided where such marks would remain on fabricated material if appearances are a concern. Punched or scribed layout marks serve as fatigue crack initiation sites and thus are prohibited for material designed for fatigue.
Minimum bend radii for 90° cold forming of sheet and plate are given in Part VI Table 3-1 for various alloys and tempers. These radii are approximate and are a function of the direction of the bend line with respect to the rolling or extruding direction. Cracking of heat treated alloys is more readily avoided with the bend line perpendicular to the rolling or extrusion direction, while the opposite is true for non-heat treatable alloys.
M.2 Cutting
M.6 Finishes
M.2.1 Methods
M.6.1 Where Protective Coating Is Required
The heat of plasma arc and laser cutting tends to produce edge cracking, especially in heat treatable alloys (2xxx, 6xxx, and 7xxx series).
Examples of protective coatings include anodizing, painting, and Alclad products. The American Architectural Manufacturers Association offers these Voluntary Specification, Performance Requirements and Test Procedures for coating aluminum:
M.2.2 Edge Quality AWS D1.2 has additional requirements for edges that will be welded.
M.2.3 Re-entrant Corners Fillets reduce stresses at re-entrant corners of parts. The proper fillet radius varies depending on the part and its use. AWS D1.1:2004, the steel structural welding code, Section 5.16, requires a minimum fillet radius of 1 inch. AWS D1.2:2008, the aluminum welding code, Section 4.11.6, requires ½ in. for statically loaded members and ¾ in. for cyclically loaded members. In Specification Table 3.1, the smallest radius for attachments for which fatigue categories are provided is 2 inches. Since this Specification applies to parts of any size, it is impractical to specify a minimum radius.
M.3 Heating Alloys 535.0, 5083, 5086, 5154, and 5456 have magnesium contents greater than 3%. When such alloys are held within the temperature range of 150°F (66°C) to 450°F (230°C), they may “sensitize” and subsequently suffer exfoliation and stress corrosion cracking. The length of time in this temperature range determines the degree of sensitization to exfoliation and stress corrosion cracking. The strength of tempered metal can be reduced by exposure to elevated temperature processes (such as factory paint curing, firing of porcelain enamel coatings, and hot forming). See the commentary to Section A.3.1.1.
M.4 Holes M.4.1 Fabrication Methods The prohibition against punching parts thicker than the hole diameter is to guard against break-out at the back side of the hole. II-40
AAMA 2603 Pigmented Organic Coatings on Aluminum Extrusions and Panels AAMA 2604 High Performance Organic Coatings on Aluminum Extrusions and Panels AAMA 2605 Superior Performing Organic Coatings on Aluminum Extrusions and Panels. Where water is allowed to stand between aluminum parts in contact, oxidation called water staining may result. While this oxidation has little or no effect on material strength and will not progress after the water is removed, it is unsightly and difficult to remove. It can be prevented by keeping aluminum dry or out of contact with other aluminum parts when moisture can be present.
M.6.2 Surface Preparation Proper surface preparation is required for good paint adherence.
M.6.3 Abrasion Blasting Abrasion blasting can be used to clean material or finish the surface. Abrasive media includes steel grit, silica sand, aluminum oxide, crushed walnut shells, or coal slag. Peening can be used to improve fatigue strength by introducing compressive stress near the surface and is typically achieved with steel or stainless steel shot. Residual stresses from blasting or peening can curl thin material. Abrasion blasting may also reduce the thickness of material. Consideration should be given to the effect on strength if the thickness is reduced by more than standard mill tolerances for the material. January 2010
M.7 Contact with Dissimilar Materials Isolators such as Teflon, neoprene, and 300 series stainless steel may be placed between aluminum and other materials to prevent contact. The isolator should be nonporous to avoid trapping water or other substances in the joint and compatible with both the aluminum and the dissimilar material in the intended service.
M.7.1 Steel Coating the steel is usually more effective than coating the aluminum to prevent galvanic corrosion between aluminum and steel.
M.7.2 Wood, Fiberboard, or Other Porous Materials Wood that has been treated with preservatives is usually corrosive to aluminum. Chromated copper arsenate (CCA) treated wood is about twice as corrosive to aluminum as non-treated wood. Residential use of CCA treated wood ended in 2003 and was replaced by alkaline copper quaternary (ACQ) treated wood, which is about four times as corrosive to aluminum as untreated wood.
M.7.3 Concrete or Masonry To avoid staining and surface corrosion, mill finished aluminum and anodized aluminum should be protected from uncured concrete, mortar, and similar alkaline substances and muriatic acid used in cleaning concrete and masonry. Masonry products designed to remain at a relatively low pH during and after curing (such as magnesium phosphate grout, which does not exceed a pH of 8.5) do not corrode aluminum.
in the shop or in an enclosure because shielding gas must cover the arc and wind can disrupt the shield. Groove welds (Figure CM.9.1) are utilized for butt joints. Groove welds are shaped for ease of root penetration, to allow for less dilution of the filler by the base metal (where hot cracking is a problem), or to permit a desirable sequence of weld bead depositions when welding in other than flat positions. Fatigue strength can be significantly increased by removing weld reinforcement. Fillet welds (Figure CM.9.2) are used to join surfaces to each other in lap, T, or corner joints; the filler usually determines the strength of these joints. A sounder and more economical structure results from using continuous welds rather than intermittent ones. While an intermittent weld may reduce welding time, filler wire consumption, heat input and/or distortion, it may produce unfavorable local stress concentrations. The possibility for poor weld quality and end craters increases with the repeated stopping and restarting of the welding. Since the cost of fillet welds is a function of the square of their size, large intermittent welds are not as efficient in carrying loads as small continuous fillets. Intermittent welds also make a structure more susceptible to moisture infiltration, which may ultimately lead to corrosion. Fillet welds exhibit different strengths depending on the geometry of the part and the type of loading on the weld. The filler shear strengths in the Specification are based
M.7.4 Runoff from Heavy Metals Heavy metals can cause deposition corrosion of aluminum. Copper is the most common of these of metals used in construction, but terne-coated steel (which has a lead/tin coating) may also have this effect.
M.8 Fabrication Tolerances The L/960 straightness tolerance was chosen so that the reduction in buckling strength versus a perfectly straight member is no greater than about 20%. The standard tolerance for some mill products does not meet the L/960 straightness tolerance for fabricated members required here (Aluminum Association (2009)). (An example is T6511 extrusions with wall thicknesses less than 0.095 in.). Such members may require additional straightening or tighter tolerance specifications to meet the requirements of this Section.
M.9 Welding AWS D1.2 provides requirements for qualifying, fabricating, and inspecting aluminum welds. Welding is done January 2010
Figure CM.9.1 II-41
a. Longitudinal Fillet
b. Transverse Fillet
c. Corner Weld
Figure CM.9.2 on tests of longitudinal fillet welds (see Figure CM.9.2a), which results in pure shear on the throat of the weld. Transverse welds (Figure CM.9.2b is one type) can have higher strengths in some cases, since the stress on the weld throat is a combination of shear and tension. This strength increase, however, is not recognized in the Specification. There are many joint details that can be utilized to improve weld performance: 1) A butt joint between different thicknesses of metal should have the thicker one beveled to match the thinner one (Figure CM.9.3). This helps balance the heat sink for uniform melting and good fusion, and reduces the stress raiser caused by change in thickness. 2) Welds may have lower strength than the base metal (e.g., welds in 6061-T6 alloy). One way to reduce the effect this has on load carrying capacity is by locating the welds in areas of low stress. Beams can be fabricated by welding together longitudinal extrusions with joints located in webs near the neutral axis (Figure CM.9.4). Since the web is often much thinner than the flanges, the amount and cost of welding are reduced. 3) Rectangular doubler plates welded on four sides have transverse welds which reduce the member’s strength. If only the sides of the doubler are welded, the longitudinal welds may become so highly stressed that they fail. When a doubler plate is necessary, it should be diamond shaped (Figure CM.9.5), avoiding a sudden cross-sectional change.
Figure CM.9.3 II-42
No welding should be done across the ends. The doublers should be as wide as possible, consistent with leaving room for a fillet weld on each side. The doubler length (l) should be greater than its width (w) by a ratio of at least 3 to 1, which orients the fillet welds nearly parallel to the stress direction. 4) When stiffening a panel or member, care should be taken to avoid abrupt changes in cross sections. Reinforcing stiffeners should have tapered ends (Figure CM.9.6) to avoid fatigue cracks at the end of the stiffener. 5) A common design issue is joining members at corners to give an economical, structurally sound, and aesthetically pleasing connection. Figure CM.9.7 illustrates corner details. Double fillets or bends to allow a butt or a lap joint should be used. 6) When sheets are to be welded to extruded members, an attempt is sometimes made to use a joint opening between sheets and make a groove weld (Figure CM.9.8). In effect,
Figure CM.9.4 January 2010
Figure CM.9.6
Figure CM.9.5 what is desired resembles a slot weld, which seldom proves practical. The joint fit and the welding procedure are both critical if the sheet edges are hot enough to melt back from the joint when the welding current is high enough to penetrate the extrusion. Therefore, conventional lap joints are recommended instead for this application.
M.10 Bolt Installation Snug tightness, a condition achieved when all plies in a joint are in firm but not necessarily continuous contact, can usually be attained by a few impacts of an impact wrench or the full effort of a person using an ordinary spud wrench.
Figure CM.9.7 January 2010
II-43
Table CM.10.1 MINIMUM BOLT TENSION FOR SLIP-CRITICAL JOINTS
Figure CM.9.8 A specific clamping force is not necessary in non-slip-critical connections because the design accounts for parts slipping relative to each other. No rules for determining the tightening torque for aluminum bolt bearing connections have been established because test results vary widely depending on the friction developed in the threads and other bearing surfaces. A recommendation sometimes made for establishing a tightening torque for aluminum bolts is as follows: Tighten several bolts of a given size and type to the breaking point under the same conditions of lubrication as will be encountered on the job and use 70% or 80% of the lowest torque obtained from the tests. The 70% value should be used for bolts that may need to be removed occasionally, while the 80% value applies to permanent bolts. Lubricating the threads and bearing surfaces is helpful. These recommendations for tightening may be modified for bolts or other threaded parts that carry fluctuating axial tensile loads that can cause fatigue failures. Under these conditions, the tightness (initial axial tensile load) should be slightly more (about 5%) than the maximum tensile load on the bolts during service. There are many devices available to prevent loosening, and guidance is available for their use (AAMA (1991)). Lock washers are commonly used; less common are locking inserts built into the nut threads. For slip-critical bolted connections, minimum bolt tensions from the RCSC Specification are given in the Table CM.10.1. Turn-of-nut tightening of slip-critical connections is performed by bringing the assembly to a snug tight condition and then applying a prescribed number of turns of the nut. Aluminum’s lower modulus of elasticity versus steel means more turns would be needed for aluminum assemblies than for steel assemblies if the bolt tension at the start of turnof-nut tightening were the same for both steel and aluminum assemblies. However, the flexibility of aluminum parts II-44
Bolt Diameter (in.)
A325 Bolt Tension (k)
½
12
5
⁄8
19
¾
28
7
⁄8
39
1
51
11⁄8
56
1¼
71
13⁄8
85
1½
103
enables them to be brought closer to full contact by snug tightening than steel, resulting in higher bolt tension in aluminum assemblies at the beginning of turn-of-nut tightening. The net effect, confirmed by testing, is that aluminum assemblies require approximately the same number of turns as steel assemblies after the snug tight condition is attained to reach the bolt tension prescribed above. Galvanizing increases the friction between the bolt and nut threads and makes torque-induced tension more variable, but lubrication both reduces the torque and makes it more consistent. Therefore, ASTM A 325 requires that a galvanized bolt and lubricated galvanized nut be assembled in a steel joint with a galvanized washer and tested in accordance with ASTM A 563 by the manufacturer prior to shipping to assure that the fastener can be rotated beyond the required rotation from the snug-tight condition without breaking. Since some lubricants are water soluble, galvanized bolts and nuts should be shipped in plastic bags in wood or metal containers.
M.11 Riveting M.11.1 Driven Head Rivet head styles are shown in the 2005 ADM, Part VII, Table 5-6. Part VII, Table 5-13 provides maximum rivet grips for given lengths for flat driven heads.
M.11.2 Hole Filling Recommended hole sizes for cold-driven rivets are shown in the 2005 ADM, Part VII, Table 5-8. Rivet lengths are given in Part VII, Table 5-12 for various grips and diameters.
M.12 Erection Tolerances Erection tolerances are often expressed in terms of tolerances on the plumbness and levelness of structural members. The erection tolerances specified on the construction documents must match the tolerances used for the stability analysis performed in accordance with Chapter C. January 2010
Appendix 1 Testing 1.1 General Provisions An example of a nationally recognized accreditation service is the International Code Council’s (ICC) International Accreditation Service (IAS). The ICC publishes the International Building Code.
1.3 Number of Tests and the Evaluation of Test Results 1.3.1 Tests for Determining Mechanical Properties Equation 1.3-1 is from Goepfert (1994). Values for K are taken from Juran (1988) and are one-sided factors affording 95% confidence that at least 99% of the popula-
January 2010
tion would fall above the predicted minimum value. Johnson (1994) provides K values for several n values greater than 100, including K = 2.326 for n = infinity. (See Section A.3.2 for discussion of the statistical basis for mechanical properties of aluminum alloys).
1.3.2 Tests for Determining Structural Performance Provisions in Section 1.3.2 are similar to those in AISI (2001).
1.4 Testing Roofing and Siding Deflection limits for roofing and siding tests should be selected accounting for the possibility of ponding.
II-45
Appendix 3 Design for Fatigue 3.1 General Provisions Sanders and Day (1983) studied fatigue behavior of aluminum weldments. Sanders and Fisher (1985) provided the fatigue provisions that appeared in the 1986 Specifications for Aluminum Structures. These provisions were subsequently revised based on work by Menzemer (1992) on full scale welded beams and by Kosteas, et al. (1985). The major factors affecting fatigue behavior are the number of stress cycles, the magnitude of the stress range, and the type and location of the member or detail. Fatigue cracks generally grow perpendicular to the plane of maximum stress. This Specification uses a nominal stress range determined by elastic analysis. The effect of stress concentrations are accounted for by the proper selection of fatigue details. Many other factors, including temperature, corrosive substances, weld defects, and post-weld mechanical treatment can have an effect on fatigue strength but are not addressed by this Specification. If information on the number of stress cycles is available for similar structures of materials other than aluminum, the same values may be used for aluminum structures. Wind-induced vibrations of undamped structures or components can cause large numbers of cycles and high stresses and thus should be avoided. Vibration dampers may be used to limit wind-induced vibrations. Vibration of structures caused by unbalanced forces from machinery can be minimized by the use of properly designed vibration mounts and proper design of the structure. If the loading frequency is between 1/2 and 2 times the natural frequency of a structure, damping should be considered (Sharp (1993)). The fatigue strength of mechanically fastened connections with a stress ratio less than or equal to zero is based on Atzori, et al. (1997), who considered data from about 750 tests of bearing and friction joints with a wide variety of conditions. The data used to determine the fatigue strength of joints with a stress ratio of zero conservatively include numerous tests with a stress ratio of 0.1. Azzam and Menzemer (2006) established the fatigue strength for detail category F1. The use of S-N curves given in the Specification is the most common but is only one of four methods of designing for fatigue. The others are hot spot (addressed by Sharp (1996a, 1996b)), strain-life, fracture mechanics, and good practice design methods. Fatigue-resistant joints can be made using gradual changes in geometry of components and joints and avoiding areas of concentrated load and stress. Because most fatigue failures initiate at areas of localized high stress, particularly joints, these details should be designed carefully. Two approaches to address this are given below. • Joints may be eliminated by using extrusions, thus removing sites for fatigue crack initiation. Sometimes the designer can locate joints or discontinuities in areas of low stress to improve fatigue resistance. II-46
• Joints can be enhanced to improve fatigue strength. These include shaping the weld toes and peening the edges of the welds. Adhesives can be employed in mechanically fastened (and spot welded) joints. Tests are required to establish fatigue strength in such cases. See Section M.6.3 for the use of peening to improve fatigue life.
3.2 Constant Amplitude Loading The allowable stress range is based on a 95% confidence for 97.7% probability of survival. The constant amplitude fatigue limit was assumed to occur at 5 × 106 cycles for each detail except category F1. This Specification’s static strength provisions limit the allowable stress range for low numbers of cycles.
3.3 Variable Amplitude Loading Actual load histories are frequently more complicated than the constant amplitude loading addressed in Section 3.2. Section 3.3 provides a design method for the variable amplitude loadings experienced by many structures. This equivalent stress method is based on nominal stress ranges, linear damage accumulation, and no sequencing effects. The rainflow method (Fuchs and Stephens (1980), Smith, et al. (1988)) is a commonly used cycle-counting method. The equation for the equivalent stress range is derived from Miner’s Rule when the S-N curve is a straight line in log-log space. Miner’s rule is ___ Σ ni≤ 1.0 Ni
(3.3-1)
where ni = number of cycles of the ith stress range Ni = number of cycles constituting failure at the ith stress range. When this fraction approaches unity, some of the details within the group have begun to fail. Miner’s rule may be used over the equivalent stress range to assess the remaining life of an existing structure or when fatigue data is not linear in the log(stress)-log(life) space. Allowable stress ranges for variable amplitude fatigue are determined in the same manner as for constant amplitude fatigue except that the constant amplitude fatigue limit is not used because data for variable amplitude loads show continuing strength decrease at long lives. Structures subjected to variable amplitude loading may not exhibit a fatigue limit because a crack can be initiated by the higher stress cycles of the spectrum and propagate at stresses below the fatigue limit. There also may not be a fatigue limit in mechanical connections that fail by fretting, whereby relative movement of the connected parts causes part wear to occur. Tests may be required to evaluate the possibility of fretting failures. January 2010
Figure C3.2 SCHEMATIC FATIGUE CURVE
January 2010
II-47
Appendix 4 Design for Fire Conditions 4.1 General Provisions This appendix is similar to the AISC (2005) appendix on design for fire conditions. While aluminum is noncombustible as determined by ASTM E 136 tests, aluminum strengths and stiffness are less at elevated temperatures than at room temperature.
4.1.3 Load Combinations and Required Strength The analysis must be performed in accordance with the requirements of Chapter C.
4.2 Design for Fire Conditions by Analysis 4.2.3 Material Properties at Elevated Temperatures Eurocode 9 Part 1-2 provides additional information on aluminum material properties at elevated temperatures.
Strengths at elevated temperatures are a function of time at the elevated temperature. The strengths given in Table 4.2 are from Kaufman (1999) for 10 hours at the elevated temperature. Kaufman provides test data for additional alloy-tempers. 4.2.3.2 Thermal Expansion The coefficient of thermal expansion increases with temperature and does not vary significantly by alloy. 4.2.3.3 Specific Heat Specific heats increase with temperature. Aluminum Standards and Data (2009) Table 2.3 provides thermal conductivities for aluminum alloys at room temperature. Thermal conductivities vary by alloy and temper and increase with temperature.
4.2.3.1 Mechanical Properties The modulus of elasticity Em at elevated temperatures is not a function of time at the elevated temperature. The moduli given by Table 4.1 are from Kaufman (1998).
Appendix 5 Evaluation of Existing Structures 5.4 Evaluation by Load Testing The procedure for evaluating existing structures by load testing is intended to produce no permanent deformation. The International Building Code 2009 section 1714.3.2 requires that existing structures be load tested to 2 times the design load. This would exceed safety factors used for aluminum
II-48
building structures (1.65 on yield and 1.95 on collapse). The test load is therefore limited to a factored load of 1.0D + 1.4L, which is approximately 85% of the LRFD load combination 1.2D + 1.6L. ACI uses 85% of their factored loads. The load factor for wind, snow, or rain loads should be the same as for live load when determining the test load.
January 2010
Appendix 6 Design of Bracing for Columns and Beams 6.1 General Provisions The provisions of this appendix are based on recommendations given in the SSRC Guide (Ziemian (2010)), and are similar to those in the AISC Specification for Structural Steel Buildings Appendix 6. See the commentary to AISC Appendix 6 for additional information on these provisions. Bracing requirements are based on a member with an initial out-of-straightness due to lateral forces and fabrication or erection tolerances of L/500. If initial out-of-straightness is greater than L/500, the brace force should be increased in direct proportion to the increase in initial out-of-straightness. Torsional bracing of beams is based on an initial twist of 1°. Appendix 6 addresses two types of bracing systems: relative and nodal. These bracing systems are described in the SSRC Guide.
6.2 Column Bracing For nodal bracing, the required bracing stiffness is a function of the number of braces. The required bracing stiffness given in Section 6.2 is conservative, being for the case of
January 2010
many braces, and is twice the stiffness required for one intermediate brace.
6.3 Beam Bracing Beam bracing must control twist of the section, but need not prevent lateral displacement. Both lateral bracing attached to the compression flange of a beam or torsional bracing can control twist. 6.3.2.1 Nodal Bracing If bsec < bT, bTb determined from Equation 6-10 is negative, indicating that torsional beam bracing will not be effective due to inadequate web distortional stiffness.
6.4 Beam-Column Bracing The bracing requirements for compression and those for flexure are superimposed to arrive at the requirements for beam-columns.
II-49
References AASHTO (1991), Guide Specifications for Aluminum Highway Bridges, Washington, DC, 1991. AASHTO (1998), AASHTO LRFD Bridge Design Specifications, Washington, DC, 1998. AASHTO (2009) Standard Specifications for Structural Supports for Highway Signs, Luminaires, and Traffic Signals, Washington, DC, 2009. Abramson, A. B. (1977), “Inelastic Torsional-Flexural Buckling of Aluminum Sections,” Report No. 365, Department of Structural Engineering School of Civil and Environmental Engineering, Cornell University, Ithaca, NY, October 1977. AISC (2005), Specification for Structural Steel Buildings, American Institute of Steel Construction, Chicago, IL. AISI (1986), Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC. AISI (2001), North American Specification for the Design of Cold-Formed Steel Structural Members, American Iron and Steel Institute, Washington, DC. Aluminum Association (2009), Aluminum Standards and Data, Alexandria, VA. Aluminum Formed-Sheet Building Sheathing Design Guide (1969), Paper 6744, Volume 95, No. ST8, Journal of the Structural Division, ASCE, August, 1969. American Architectural Manufacturers Association (1991), AAMA TIR-A9-91 Metal Curtain Wall Fasteners, 1991, Schaumberg, IL. American Architectural Manufacturers Association (2000), AAMA TIR-A9-91 (2000 Addendum) Metal Curtain Wall Fasteners Addendum, 2000, Schaumberg, IL. Anderson, J. M. and Trahair, N. S. (1972), “Stability of Monosymmetric Beams and Cantilevers,” Journal of the Structural Division, ASCE, January, 1972. ASCE (1956), Committee of The Structural Division on Designing Lightweight Structural Alloys, “Specifications for Structures of Aluminum Alloy 2014-T6,” Paper 971, Journal of the Structural Division, ASCE, Vol. 82, No. ST3, May, 1956. ASCE (1962a), Task Committee on Lightweight Alloys, “Suggested Specifications for Structures of Aluminum Alloys 6061-T6 and 6062-T6,” Paper 3341, Journal of the Structural Division, ASCE, Vol. 88, No. ST6, December, 1962. ASCE (1962b) Task Committee on Lightweight Alloys, “Suggested Specifications for Structures of Aluminum Alloy 6063-T5 and 6063-T6,” Paper 3342, Journal of the Structural Division, ASCE, Vol. 88, No. ST6, December, 1962. ASCE (1969), Task Committee on Lightweight Alloys, “Guide for the Design of Aluminum Formed-Sheet Building Sheathing,” Journal of the Structural Division, ASCE, Vol. 95, No. ST6, August, 1969, p. 1727. ASME (1989), B1.1-1989 Unified Inch Screw Threads, New York, NY. II-50
Atzori, B., Lazzarin, P., and Quaresimin, M. (1997), “A Re-Analysis on Fatigue Data of Aluminum Alloy Bolted Joints,” International Journal on Fatigue, Vol. 19, No. 7, 1997. AWS (2008), D1.2 Structural Welding Code—Aluminum, Miami, FL. Azzam, D. and Menzemer, C. C. (2006), “Fatigue Behavior of Welded Aluminum Light Pole Support Details,” Journal of Structural Engineering, ASCE, Volume 132, No. 12, December 2006, pp. 1919–1927. Battdorf, S. B., Stein, M., and Schildcrout, M. (1947), “Critical Stress of Thin-Walled Cylinders in Torsion,” Technical Note 1344, National Advisory Committee for Aeronautics (now NASA), Washington, DC. Batterman, R. H., and Johnston, B. G. (1967), “Behavior and Strength of Metal Columns,” Journal of the Structural Division, ASCE, Vol. 93, No. ST2, April, 1967, p. 205. Bijlaard, P. P., and Fisher, G. P. (1952), “Column Strength of H-Sections and Square Tubes in Postbuckling Range of Component Plates,” Technical Note 2994, National Advisory Committee for Aeronautics (now NASA). Bleich, F. (1952), Buckling Strength of Metal Structures, McGraw-Hill. British Standards Institution (1987), British StandardStructural Use of Steelwork in Building—Part 5. Code of Practice for Design of Cold-Formed Sections, BS 5950: Part 5:1987. Brungraber, R. J., and Clark, J. W. (1962), “Strength of Welded Aluminum Columns,” Transactions ASCE, Vol. 127, Part II, p. 202, 1962. Chapuis, J., and Galambos, T. V. (1982), “Restrained Crooked Aluminum Columns,” Journal of the Structural Division, ASCE, Vol. 108, No. ST3, March 1982, p. 511. Clark, J. W., and Hill, H. N. (1960), “Lateral Buckling of Beams,” Journal of the Structural Division, ASCE, Vol. 86, No. ST7, July, 1960, p. 175. Clark, J. W., and Rolf, R. L. (1964), “Design of Aluminum Tubular Members,” Journal of the Structural Division, ASCE, Vol. 90, No. ST6, December, 1964, p. 259. Clark, J. W., and Rolf, R. L. (1966), “Buckling of Aluminum Columns, Plates, and Beams,” Journal of the Structural Division, ASCE, Vol. 92, No. ST3, June, 1966, p. 17. Conley, W. F., Becker, L. A., and Allnutt, R. B. (1963), “Buckling and Ultimate Strength of Plating Loaded in Edge Compression. Progress Report 2: Unstiffened Panels,” Report 1682, David Taylor Model Basin, U.S. Department of the Navy, Washington, DC, May, 1963. Cook, I. T., and Rockey, K. C. (1962), “Shear Buckling of Clamped and Simply Supported Infinitely Long Plates Reinforced by Transverse Stiffeners,” The Aeronautical Quarterly, Vol. 13, February, 1962, p. 41. Crockett, Harold B. (1942), “Predicting Stiffener and Stiffened Panel Crippling Stresses,” Journal of the Aeronautical Sciences, Vol. 9, November, 1942, p. 501. January 2010
Department of Defense (1994), Metallic Materials and Elements for Aerospace Vehicle Structures, MIL-HDBK-5, Washington, DC. Dewalt, W. J. and Mack, R. E. (1980), “Design Considerations for Aluminum Fasteners,” SAE Technical Paper 800455, 1980. Dux, P. F. and Kitipornchai (1986), “Elastic Buckling Strength of Braced Beams,” Journal of the Australian Institute of Steel Construction, May, 1986. Ellingwood, B. E., MacGregor, J. G., Galambos, T. V., and Cornell, C. A., (1982) “Development of a ProbabilityBased Load Criteria: Load Factors and Load Combinations,” Journal of the Structural Division, ASCE, Volatile. 108, No. 5, pp. 978–997. European Convention for Constructional Steelwork, European Recommendations for the Design of Light Gage Steel Members, First Edition, 1987, Brussels, Belgium. Fortlin, D., Beaulieu D., and Bastien, J., (2001), “Experimental Investigation of Aluminum Friction-Type Connections, INALCO 8 Proceedings, Technical University of Munich, Munich, 2001. Fuchs, H. O. and Stephens, R. I. (1980), Metal Fatigue in Engineering, John Wiley & Sons, New York, NY. Galambos, T. V., (1979), Load and Resistance Factor Design for Aluminum Structures, Research Report No. 54, Washington University, St. Louis, MO. Galambos, T. V., (editor) (1998), Guide to Stability Design Criteria for Metal Structures, Structural Stability Research Council, 5th edition, John Wiley and Sons, New York, NY. Gaylord, E. H., Gaylord, C. N., and Stallmeyer, J. E. (1992), Design of Steel Structures, 3rd edition, McGraw-Hill, NY. Gerard, George, and Becker, Herbert (1957), Handbook of Structural Stability, Part l-Buckling of Flat Plates, Technical Note 3781, National Advisory Committee for Aeronautics (now NASA). Goepfert, W. P. (1994), “Statistical Aspects of Mechanical Property Assurance,” Aluminum and Magnesium Alloys, ASTM Volume 02.02. Hartmann, E. C., and Clark, J. W. (1963), “The U.S. Code,” Proceedings of the Symposium on Aluminum in Structural Engineering, The Institution of Structural Engineers and the Aluminum Federation, London, 1963. Hill, H. N., Clark, J. W., and Brungraber, R. J. (1962), “Design of Welded Aluminum Structures,” Transactions ASCE, Vol. 127, Part II, p. 102. Hill, H. N., Hartmann, E. C., and Clark, J. W. (1956), “Design of Aluminum Alloy Beam-Columns,” Transactions ASCE, Vol. 121, 1956, p 1. Johnson, R. A. (1994), Miller and Freund’s Probability and Statistics for Engineers, 5th edition, Prentice-Hall, Englewood Cliffs, NJ. Jombock, J. R., and Clark, J. W. (1968), “Bending Strength of Aluminum Formed Sheet Members,” Journal of the Structural Division, ASCE, Vol. 94, No. ST2, February, 1968, p. 511. Juran, J. M. (1988), Juran’s Quality Control Handbook, 4th ed., McGraw-Hill, New York. January 2010
Kaufman, J. G. (1999), Properties of Aluminum Alloys, ASM International, Materials Park, OH. Kaufman, J. G. (2001), Fracture Resistance of Aluminum Alloys, ASM International, Materials Park, OH. Kim, Yongwook (2003), Behavior and Design of Aluminum Members in Bending, Cornell University, Ithaca, NY. Kirby, P. A. and Nethercot, D. A. (1979), “Design for Structural Stability,” Constrado Nomographs, A Halstead Press Book, John Wiley & Sons, New York, NY. Kissell, J. R. and Ferry, R. L. (1997), “Aluminum Friction Connections,” Proceedings of Structures Congress XV, April, 1997. Kitipornchai, S., Wang, C. M. and Trahair, N. S. (1986), “Buckling of Monosymmetric I-Beams Under Moment Gradient,” Journal of the Structural Division, Vol. 112, No. ST4, April, 1986, ASCE, pp. 781–799. Kosteas, D., Polas, K. and Graf, U. (1985), “Results of the Welded Beam Program,” Third International Aluminum Conference, Munich, 1985. LaBelle, James C. and Dolby, Tanya (2004), “Flat Head Fastener Pullover in Thin Aluminum with Countersunk Holes,” 2004 International Aluminum Connections Conference, Cleveland, OH. LaBelle, James C. and Dolby, Tanya (2009), Light Metal Age, “Hex Washer-Head Fastener Pull-Over in Moderately Thin Aluminum,” April 2009, Vol. 67, No. 2, South San Francisco, CA. Luttrell, C. R. (1999), “Thermal Cycling of Slip-Critical Aluminum Joints,” Proceeding of Structures Congress XVII, American Society of Civil Engineers, Reston, VA, April, 1999. Marsh, Cedric, (1979), “Tear-out Failures of Bolt Groups,” Technical Notes, Journal of the Structural Division, Proceedings of the American Society of Civil Engineers, October, 1979. Massonnet, C. E. L. (1962), “Stability Considerations in the Design of Steel Plate Girders,” Transactions ASCE, Vol. 127, Part II 1962, p. 420. May, James E. and Menzemer, C. C. (2005), “Strength of Bolted Aluminum Alloy Tension Members,” Journal of Structural Engineering, ASCE, Vol. 131, No. 7, p. 1125. Menzemer, C. and Iasconne, R. (2002), “Reestablishing the Shear Strength of Aluminum Alloy Fillet Welds,” Welding Journal, April, 2002. Menzemer, C. C. (1992), Fatigue Behavior of Welded Aluminum Structures, Dissertation for the Degree of Doctor of Philosophy, Lehigh University, Bethlehem, PA. Menzemer, C. C., Ortiz-Morgado, R., Iascone, R., and Srivatsan, T. (2001), INALCO 2001, Bearing Capacity of Aluminum Alloys in Bolted Connections, Munich. Menzemer, Craig (1999), “Failure of Bolted Connections in an Aluminum Alloy,” Journal of Materials Engineering and Performance, ASM, Vol. 8, No. 2, April, 1999. Menzemer, C. C., Deliwala, J., and Kissell, J. R. (2008), Light Metal Age, “Pull-Out Strength of Self Tapping Fasteners in Aluminum Screw Slot Connections,” September/October 2008, Volume 66, No. 5, South San Francisco, CA. II-51
Moisseiff, Leon S., Hartman, E. C. and Moore, R. L. (1944), “Riveted and Pin-Connected Joints of Steel and Aluminum Alloys,” Transactions ASCE, Vol. 109, 1944, p. 1359. Moore, R. L. (1942), “An Investigation of the Effectiveness of Stiffeners on Shear-Resistant Plate-Girder Webs,” Technical Note 862, National Advisory Committee for Aeronautics (now NASA), Washington, DC. Moore, R. L. (1947), “Observations on the Behavior of Aluminum Alloy Test Girders,” Transactions ASCE, Vol. 112, 1947, p. 901. Moore, R. L., Jombock, J. R., and Kelsey, R. A. (1971), “Strength of Welded Joints in Aluminum Alloy 6061-T6 Tubular Members,” The Welding Journal, April, 1971. Nelson, F. G. Jr., and Howell, F. M. (1952), “The Strength and Ductility of Welds in Aluminum Alloy Plate,” The Welding Journal, September, 1952. Nelson, F. G. Jr., and Rolf, R. L. (1966), “Shear Strength of Aluminum Alloy Fillet Welds,” The Welding Journal, February, 1966. Peköz, T. (1990), “Designs of Cold-Formed Steel Screw Connections,” Proceedings of the Tenth International Specialty Conference on Cold-Formed Steel Structures, October 23–24, 1990, University of Missouri-Rolla, MO. Roark, R. J. and Young, W. C. (1989), Formulas for Stress and Strain, McGraw-Hill. Rockey, K. C. (1958), “Web Buckling and the Design of Web Plates,” The Structural Engineer, February, 1958, p. 45. Sanders, W. W. and Fisher, J. W. (1985), Recommended Specifications for Fatigue Design of Aluminum Structures, Submitted to the Aluminum Association, Washington, DC. Sanders, W. W. and Day, R. H., (1983) Fatigue Behavior of Aluminum Alloy Weldments, Welding Research Council Bulletin 286. Schilling, C. F. (1965), “Buckling Strength of Circular Tubes,” Journal of the Structural Division, ASCE, Vol. 91, No. ST5, October, 1965, p. 325. Sharp, Maurice L. (1966), “Longitudinal Stiffeners for Compression Members,” Journal of the Structural Division, ASCE, Vol. 92, No. ST5, October, 1966, p. 187. Sharp, Maurice L. (1970), “Strength of Beams or Columns with Buckled Elements,” Journal of the Structural Division, ASCE, Vol. 96, No. ST5, May, 1970, p. 1011. Sharp, M. L. (1973), “Static and Dynamic Behavior of Welded Aluminum Beams,” Supplement to the Welding Journal, February, 1973. Sharp, Maurice L. (1993), Behavior and Design of Aluminum Structures, McGraw-Hill, New York, NY.
II-52
Sharp, M. L., and Clark. J. W. (1970), “Thin Aluminum Shear Webs,” Preprint No. 1237, ASCE, 1970. Sharp, M. L., Rolf. R. L., Nordmark, G. E., and Clark, J. W. (1982), “Tests of Fillet Welds in Aluminum,” The Welding Journal, April, 1982. Sharp, M. L., Nordmark, G. E., and Menzemer, C. C. (1996a) “Hot-Spot Fatigue Design of Aluminum Joints,” Proceedings of the 1996 ASCE Materials Engineering Conference, Washington, DC. Sharp, M. L., Nordmark, G. E., and Menzemer, C. C. (1996b) Fatigue Design of Aluminum Components and Structures, McGraw-Hill, Inc., New York, NY. Smith, I. F. C., Castiglioni, C. A. and Keating, P. B. (1988), “An Analysis of Fatigue Recommendations Considering New Data,” Proceedings IABSE Meeting, December 1988. Sooi, T. K. and Peköz, T. (1993), “Behavior of Component Elements of Aluminum Members,” Research Report No. 93-1, School of Civil and Environmental Engineering, Cornell University, Ithaca, NY. Templin, R. L., Sturm, R. G., Hartmann, E. C., and Holt, M. (1938), Column Strength of Various Aluminum Alloys, Alcoa Research Laboratories Technical Paper No. 1, Aluminum Co. of America, Pittsburgh, PA. Texas Transportation Institute (1980), An Investigation of the Strength of Welds Used in Aluminum Lighting Poles, Final Report for the Spun Aluminum Pole Group of the National Electrical Manufacturers Association, College Station, TX. Wang, C. M. and Kitipornchai, S. (1986), “Buckling Capacities of Mono Symmetric I-Beams,” Journal of the Structural Division, ASCE, Vol. 112, No. ST11, November, 1986, pp. 2373–2391. Wang, C. M. and Kitipornchai, S. (1986), “On the Stability of Monosymmetric Cantilevers,” Eng. Structures, Vol. 8, July, 1986. Weingarten, V. I., Morgan, E. J., and Seide, Paul (1965), “Elastic Stability of Thin Walled Cylindrical and Conical Shells Under Axial Compression,” AIAA Journal, Vol. 3, No. 3, March, 1965, p. 500. Winter, G. (1941), in “Lateral Stability of Unsymmetrical I Beams and Trusses in Bending,” ASCE Transactions, Paper No. 2178, December, 1941. Ziemian, Ronald (editor) (2010), Guide to Stability Design Criteria for Metal Structures, Structural Stability Research Council, 6th edition, John Wiley and Sons, Hoboken, NJ.
January 2010
Aluminum Design Manual
PART III Design Guide
III Design Guide TABLE OF CONTENTS 1 . Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 2. General Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1 Aluminum’s Attributes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Alloy Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Comparing Aluminum and Steel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4.1 General. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4.2 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4.3 Alloys and Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.4 Automotive. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.5 Bridges and Highway Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.6 Rail Cars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.7 Ships. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.8 Storage Tanks, Pressure Vessels, and Pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.9 Material Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.10 Foreign Codes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3. Structural Issues not Addressed in the Specification for Aluminum Structures. . . . . . . . . . . . . . . . . . . . . 9 3.1 Ductility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 Shear Diaphragms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Pipe Bursting Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Biaxial and Triaxial Stresses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.5 Aluminum Composite Material (ACM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4. Adhesive Bonded Joints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.1 Advantages and Disadvantages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2 Adhesive Selection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 Types of Adhesives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.4 Surface Pretreatments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.5 Joint Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.6 Current Adhesive Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 5. Extrusion Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5.1 Replacing Fabrications with Extrusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 5.2 Design Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5.3 Design Guidelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.4 Design for Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 6 . Preventing Corrosion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 7 . Fire Protection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25 8. Sustainability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.1 Reflectance and Emittance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 8.2 Recycling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 9 . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
January 2010
III-3
1. Introduction This part of the Aluminum Design Manual addresses aluminum structural design issues not addressed in Part I, the Specification for Aluminum Structures. The strength equations given in Part I may be applied to the design of any structural components, including buildings, bridges, ships, rail cars, automobiles, trucks, highway
January 2010
structures, and machinery. For example, the equations for a column given in the Specification apply equally to a column for a patio roof, a member in a latticed roof, a strut in a rail car or automobile, a member in a bridge truss, and a stanchion or pillar in a ship.
III-5
2. General Considerations 2.1 Aluminum’s Attributes Aluminum has many attributes that make it a costeffective structural material. Most applications make use of a favorable life cycle cost, which includes costs for material, fabrication, erection or installation, operation, maintenance, and disposal. For example, aluminum is the principal material in aerospace structures, primarily because of its high strengthto-weight ratio. The density of aluminum is about ¹⁄³ that of steel, and aluminum alloys have strengths similar to those of construction steels. Aluminum aerospace structures are cost effective because smaller engines and less fuel are needed during service compared to those required for heavier structures. Aluminum structures generally weigh ¹⁄³ to ½ those of steel (see Section 2.3). Light weight and corrosion resistance are the major factors for the selection of aluminum for trucks, automobiles, and rail cars. Aluminum’s excellent corrosion resistance (see Section 6) helps reduce maintenance costs. Aluminum’s corrosion resistance and its appearance, bare or finished, are major factors in its use in buildings. Many aluminum structures, such as light poles, overhead sign trusses, latticed roofs, and bridges do not require painting because of aluminum’s corrosion resistance.
2.2 Alloy Selection Sheet, plate, extrusions, forgings, and castings are made of aluminum. Alloys and tempers with both good strength and corrosion resistance are available. Aerospace alloys are generally not used for other types of structures because
their combination of specialized properties results in relatively higher costs than that of other alloys. Examples of some of the common alloys and tempers used for each product are given in the following table. Product Sheet and Plate
Extrusions Forgings Castings
Application Building Heavy Duty Structures Building General Purpose Wheels General Purpose High Elongation
Alloys 3105-H25, 5052-H34, 3004-H16 5083-H116, 5086-H116, 6061-T6 6063-T5, 6063-T6 6061-T6 6061-T6 356.0-T6, A356.0-T6 A444.0-T4
2.3 Comparing Aluminum and Steel Aluminum structural design is very similar to that for steel and other metals. Because many engineers are more familiar with steel than aluminum, aluminum and steel are compared in Table 2-1, taken from Sharp (1993). Because of the difference in properties (modulus, for example) an aluminum design should be different than that for steel in order to use material efficiently. Figure 2-1 shows the relative weights of aluminum and steel box beams with the same bending strength and deflection. The yield strength of the two materials is the same. The aluminum part weighs about 50% of the steel part when its size is about 1.4 times that of steel. Other configurations provide less weight savings. Where deflection and fatigue considerations control the design, such as in bridge girders, automotive frames and
Table 2-1 COMPARING ALUMINUM AND STEEL Property
Steel
Aluminum
Importance for Design
Modulus of elasticity
29 × 103 ksi
10.1 × 103 ksi
Deflection of members Vibration Buckling
Weight per volume
0.284 lb/in3
0.10 lb/in3
Weight of Product, Vibration
Thermal expansion
7 × 10-6/°F
13 × 10-6/°F
Thermal expansion Thermal stress
Stress-strain curves
Varies
Varies
Depends on alloys Steel often has higher strength and elongation at room temperature Aluminum has better performance at low temperatures
Fatigue Strength
Varies
Varies
For joints, aluminum has about ¹⁄³ to ½ the fatigue strength as steel for same detail
Corrosion resistance
Needs protection
Often used unpainted
Aluminum usually is maintenance free Aluminum is non-staining
Strain rate effects on mechanical properties
High strain rates increase properties—varies with type of steel
Much less change in properties compared to steel
Need to use dynamic properties for high-strain rate loadings
III-6
January 2010
Figure 2-1 MINIMUM WEIGHT OF SQUARE TUBULAR SECTIONS other transportation vehicles, aluminum structures weigh about half that of steel structures. For structures controlled by static strength, such as automobile hoods and deck lids and some building components, aluminum structures weighing about ¹⁄³ that of steel have been achieved. Such structures are designed for aluminum and do not have the same dimensions as the steel structure. Figure 2-2 shows fatigue strengths for aluminum and steel for groove welds (a Category C detail). For long lives the fatigue strength of aluminum groove welds is about 40% that for steel. The difference is smaller at shorter lives. In efficient designs, aluminum components are different from steel components for the same loading. Aluminum
beams should be deeper than steel beams. The spacing of stiffeners on aluminum elements should be smaller than for steel. These geometrical differences will help meet deflection requirements for aluminum components and reduce stresses, helping with fatigue requirements.
2.4 References The following references are additional sources of information on aluminum structural design. References marked * are available from the Aluminum Association (www.aluminum. org/bookstore). References marked ** are available for free download from the Aluminum Association at www.auto aluminum.org.
2.4.1 General *1. Kissell, J. Randolph, and Ferry, Robert L., Aluminum Structures, 2nd ed., John Wiley & Sons, New York, NY, 2002. 2. Sharp, Maurice L., Behavior and Design of Aluminum Structures, McGraw-Hill, Inc., New York, NY, 1993. 3. Sharp, M. L., Nordmark, G. E., and Menzemer, C. C., Fatigue Design of Aluminum Components and Structures, McGraw-Hill, Inc., New York, NY, 1996.
2.4.2 Fabrication
Figure 2-2 FATIGUE DESIGN CURVES FOR ALUMINUM AND STEEL January 2010
*1. Forming and Machining Aluminum, Aluminum Association, Washington, DC, 1988. *2. AWS D1.2/D1.2M:2008 Structural Welding CodeAluminum, American Welding Society, Miami, FL, 2008. III-7
*3. Welding Aluminum: Theory and Practice, 4th ed., Aluminum Association, Washington, DC, 2002. *4. Minford, J. Dean, Handbook of Aluminum Bonding Technology and Data, Marcel Dekker, Inc., New York, NY, 1993.
2.4.3 Alloys and Products *1. Aluminum Standards and Data, 2009, Aluminum Association, Arlington, VA, 2009. *2. Aluminum Standards and Data Metric SI 2009, Aluminum Association, Arlington, VA, 2009. *3. Standards for Aluminum Sand and Permanent Mold Castings, Aluminum Association, Arlington, VA, 2008. *4. AWS A5.10/A5.10M: 1999 (R2007) Specification for Bare Aluminum and Aluminum-Alloy Welding Electrodes and Rods, American Welding Society, Miami, FL, 2007.
2.4.4 Automotive **1. AT3 Aluminum for Automotive Body Sheet Panels, Aluminum Association, Washington, DC, 1998. **2. AT4 Practices for the Repair of Automotive Sheet Aluminum, Aluminum Association, Washington, DC, 1998. **3. AT5 Automotive Aluminum Crash Energy Management Manual, Aluminum Association, Washington, DC, 1998. **4. AT6 Aluminum Automotive Extrusion Manual, Aluminum Association, Washington, DC, 1998.
2.4.5 Bridges and Highway Structures 1. AASHTO LRFD Bridge Design Specifications, 2nd ed., American Association of State Highway and Transportation Officials, Washington, DC, 1998. 2. Guide Specifications for Aluminum Highway Bridges, American Association of State Highway and Transportation Officials, Washington, DC, 1991. 3. Standard Specifications for Structural Supports for Highway Signs, Luminaires and Traffic Signals, American Association of State Highway and Transportation Officials, Washington, DC, 2009.
2.4.6 Rail Cars 1. Manual of Standards and Recommended Practices Section C, Part II, Design, Fabrication, and Construction of Freight Cars, Association of American Railroads, Transportation Technology Center, Pueblo, CO. 2. AWS D15.1:2007 Railroad Welding Specification— Cars and Locomotives, American Welding Society, Miami, FL, 2007.
III-8
2.4.7 Ships *1. ANSI/AWS D3.7-2004 Guide for Aluminum Hull Welding, American Welding Society, Inc., Miami, FL, 2004. 2. Rules for Building and Classing Aluminum Vessels, American Bureau of Shipping, Houston, TX, 1996.
2.4.8 Storage Tanks, Pressure Vessels, and Pipe 1. ASME B31.3-2004, Process Piping, American Society of Mechanical Engineers, New York, NY, 2004. 2. ASME Boiler and Pressure Vessel Code, Section II, Materials, American Society of Mechanical Engineers, New York, NY, 2007. 3. API Standard 620, Design and Construction of Large, Welded, Low-Pressure Storage Tanks, 11th ed., American Petroleum Institute, Washington, DC, February 2008. 4. API Standard 650, Welded Tanks for Oil Storage, 11th ed., Addendum 1, American Petroleum Institute, Washington, DC, November 2008. Appendix AL addresses aluminum storage tanks. *5. Aluminum Alloys for Cryogenic Applications, Aluminum Association, Washington, DC, 1999.
2.4.9 Material Properties *1. Kaufman, J. Gilbert, Fracture Resistance of Aluminum Alloys: Notch Toughness, Tear Resistance, and Fracture Toughness, ASM International, Materials Park, OH, 2001. *2. Kaufman, J. Gilbert, Properties of Aluminum Alloys: Tensile, Creep, and Fatigue Data at High and Low Temperatures, ASM International, Materials Park, OH, 1999. 3. DOT/FAA/AR-MMPDS-02, Metallic Materials Properties Development and Standardization (MMPDS), (formerly MIL Handbook 5) Chapter 3, April 2005, U.S. Department of Transportation, Federal Aviation Administration, Washington, DC. Copies available through the National Technical Information Service (NTIS), 5285 Port Royal Road, Springfield VA 22161, http://www.ntis.gov; or http://engineers. ihs.com/collections/abstracts/MMPDS-02.htm
2.4.10 Foreign Codes 1. EN 1999-1-1:2007 Eurocode 9 Design of Aluminium Structures Part 1-1: General structural rules, European Committee for Standardization (CEN), Brussels, 2007. 2. CSA S157 Strength Design in Aluminum, Canadian Standards Association, Mississauga, Ontario, Canada, 2005.
January 2010
3. Structural Issues not Addressed in the Specification for Aluminum Structures 3.1 Ductility The accepted measure of ductility of aluminum alloys is fracture toughness and many high strength aluminum alloys used in aerospace applications have been evaluated as summarized by the Aluminum Association (1987). The ductility of alloys included in the Specification (non-aerospace alloys) is generally not a design issue for wrought products. The best proof of adequate ductility of alloys is the satisfactory service in buildings, bridges, automobiles, trucks, and rail cars. Menzemer (1992) showed that in laboratory fracture tests the normalized resistance curves (same fatigue strength) of parts made from 5456-H116 were higher than those of A36 steel at temperatures from -200 to +75 °F. Sharp (1993) provides additional information on the toughness of aluminum alloys. Welded strengths can be increased by welding in the solution heat-treated temper and then aging or by welding and then solution heat treating and aging. Light pole manufacturers typically use post-weld heat treatment. The ductility of transversely welded structures is usually reduced by post-weld heat treatment because the width of the zone of lower strength material is decreased (plastic deformation may be confined to a narrow zone). Post-weld heat treatments require careful evaluation of strength, ductility, and corrosion resistance implications.
3.2 Shear Diaphragms Shear diaphragms are efficient in carrying shear loads. Corrugated panels can be used for a building’s side or roof. The strength and stiffness of a corrugated panel subjected to shear depend on the alloy, configuration of the corrugation, size of the panel, and the type and configuration of the fastening to the framing members. Sharp presents the following design considerations: 1. Overall shear buckling of the panel may control strength. An equivalent slenderness ratio is defined for this mode of failure that is used with the buckling equations for shear. 2. Local buckling of the shear elements of the corrugations is given by the equations for unstiffened webs. 3. Failure of the corrugations and of the fastening at the supports must be calculated. Local failure of the corrugations at their attachment to supporting members can occur particularly if only part of the shape is connected. 4. Shear deflection of the panel is much larger than a flat panel of the same size. The major factors are size of panel, shape and thickness or corrugation, and the type and arrangement of the fastenings. Sharp (1993) provides equations of behavior for several standard corrugated shapes. January 2010
The Metal Construction Association’s Primer on Diaphragm Design (2004) addresses aluminum diaphragms. Sooi and Peköz (1993) provide additional information on building diaphragms and their interaction with building frames.
3.3 Pipe Bursting Pressure Sharp (1993) gives the bursting pressure of aluminum pipe as: P=
2tFtuK D – 0.8t
Where: P = bursting pressure t = pipe wall thickness Ftu = tensile ultimate strength K = 0.73 + 0.33Fty /Ftu D = pipe outside diameter Fty = tensile yield strength Aluminum pipe applications may be governed by standards for that use. For example, aluminum pipe used in chemical plants and petroleum refineries is often designed in accordance with ASME B31.3, which provides a slightly different strength equation and safety factors appropriate to such applications.
3.4 Biaxial and Triaxial Stresses The Aluminum Specification predates finite element analysis (FEA) and doesn’t directly address all issues that arise from such analyses. For example, the Specification provides design stresses for prismatic members primarily under uniaxial stress, such as columns. FEA, on the other hand, can provide triaxial stresses by reporting, in addition to longitudinal stresses, through-thickness and transverse stresses. Many FEA programs calculate a von Mises stress (explained below) from the triaxial stresses at a given element. Yielding occurs in ductile materials like aluminum when ( f1 - f2)2 + (f2 - f3)2 + (f3 - f1)2 > 2 Fty2 where f1, f2, f3 = principal stresses (the normal stress on each of three orthogonal surfaces such that the shear stresses on the surfaces are zero) Fty = tensile yield stress This equation is called the von Mises criterion or distortion energy criterion. It predicts that yielding will occur when the distortion energy equals the distortion energy in an axially loaded member at yield. The above equation is III-9
for the general triaxial stress state. If stresses are biaxial, f3 = 0, and the equation above predicts yielding when (f1 - f2)2 + f 22 + f 12 > 2 F 2ty For convenience, the von Mises stress is defined from the von Mises criterion as ____________________
√ (f - f ) + (f - f ) + (f - f ) 2
2
2
1 2 2 3 3 1 ___________________ 2
so that it may be compared directly to the yield stress to determine if yielding will occur. In the biaxial stress state, the von Mises stress becomes __________
√f 12 - f1 f2 + f 22 The von Mises criterion is used in the Aluminum Specification to determine the shear yield strength of aluminum alloys, since there is no established test method to measure shear yield strength. In the case of pure shear, the shear stresses in a biaxial stress element are t and -t. Mohr’s circle can be used to show that the principal stresses f1 and f2 are, then, also t and -t, so the von Mises stress is ____________
__
√ τ2 - τ(-τ) + τ2 = τ√3 When the von Mises stress equals Fty, yielding occurs, so shear yield ty is Fty τy = ___ __ √ 3 Local yielding in a member may not limit its usefulness if the amount of material that yields is small or positioned so as to have only a negligible effect on the shape and loadcarrying capacity of the member. Where yielding is a limit state, the von Mises stress should be limited to the yield strength of the material.
3.5 Aluminum Composite Material (ACM)
factory-manufactured panel consisting of metal skins bonded to both faces of a plastic core.” Panels with aluminum skins are called aluminum composite material (ACM) (see Figure 3-1). The IBC also defines a metal composite material system as “an exterior wall covering fabricated using MCM in a specific assembly including joints, seams, attachments, substrate, framing and other details as appropriate to a particular design.” However, ACMs are not limited to exterior applications. IBC Section 1407 provides requirements for two uses of MCM: one as exterior wall finish, and the other as architectural trim. Section 1407.4 requires that MCM exterior walls be designed for IBC Chapter 16 wind loads for components and cladding. Section 1407.5 requires that test results or engineering analysis be submitted to the building official to demonstrate this. IBC also specifies fire-resistance requirements that apply to both MCM uses. ACM panels must be designed to meet deflection limits as well as provide sufficient strength for wind loads. Typical ACM properties Property
Value
Units
coefficient of thermal expansion
13 × 10-6
/°F
available thicknesses
3, 4, and 6
mm
skin thickness
0.020
in.
Manufacturers provide additional information on loadspan-deflection, dimensional tolerances, section modulus, stiffness, weight, thermal resistance, sound transmission, and fire resistance. In a similar product, an aluminum-elastomer sandwich beam, the components comprising the structural elements also act together creating a combined strength and other characteristics that are greater than the sum of the parts. The composite beam may have to resist stresses due to a temperature gradient through the section as well as stresses from wind and dead loads. The amount of composite action can be determined by analysis (AAMA (1990)) or testing.
The 2009 International Building Code (IBC) Section 1402.1 defines metal composite material (MCM) as “a
Figure 3-1 SANDWICH PANEL III-10
January 2010
4. Adhesive Bonded Joints An adhesive can be defined as a substance capable of holding materials, similar and dissimilar, together by surface attachment. The critical substrate surfaces can be held together by chemical and/or mechanical adhesion at the interfacial layer of contact between surfaces (D.A.T.A. (1986)).
4.1 Advantages and Disadvantages Shields (1970) and Thrall (1984) address advantages and disadvantages of adhesives. Some advantages of adhesive bonding are: • Ability to bond a variety of materials that may exhibit differing coefficients of thermal expansion, moduli, thickness, etc., with proper joint design and material selection. • Improved cosmetics of the finished product by the elimination of protruding mechanical fasteners, such as rivets or bolts. • Excellent strength to weight ratio in comparison to other joining methods. • Good joint stiffness and fatigue performance, with appropriate choice of adhesive. • Elimination of stress concentrations inherent to mechanical fastening methods, and a more uniform stress distribution over the bonded surface area. • Adaptable to many production processes because of the variety of forms (pastes, films, emulsions, etc.) and methods of application of adhesives. The advantages of adhesive bonding are most evident when joining relatively thin materials and components. The cost advantages and joint efficiencies decrease as the members become thicker. Some disadvantages of adhesive bonding are: • Expert joint design is critical in order to minimize peel and/or cleavage stresses. • Temperature limitations may restrict the use of many adhesives from high temperature applications. • Adhesives require surface pretreatment of the aluminum unless the adhesive manufacturer recommends that no pretreatment is necessary. Even with this recommendation, the durability required for the application should be verified. • Difficulties in inspecting for initial bond integrity and an insufficient understanding of the effects of in-service damage on subsequent bond performance limit confidence in adhesive bonding as a primary structural joining method.
4.2 Adhesive Selection Literally thousands of commercial adhesives are available. In order to select the proper adhesive for a particular application the user needs a systematic approach to adhesive selection. Major areas to address are: January 2010
• Substrates • Pretreatment • Application of adhesive • Fabrication process • Service environments • Design
4.3 Types of Adhesives Kinloch (1987) identified two groups of adhesives: thermoplastics and thermosets. Thermoplastics are materials which can be repeatedly softened by heat and hardened by cooling to ambient temperature. Thermosets are materials that undergo chemical reactions initiated by heat, catalyst, UV light, etc. Thermosets are generally more durable than thermoplastics. From the two groups of adhesives extend several classes of adhesives, which include anaerobic, contact, cyanoacrylate, film, hot melt, one-part and two-part. Anaerobic adhesives are generally esters or acrylics in which, upon the restriction/lack of air/oxygen, curing of the adhesive initiates. Anaerobic adhesives can also be cured by UV exposure. Contact adhesives are coated to both substrate surfaces, and a solvent is allowed to evaporate before assembly of the substrates. Cyanocrylates are known as instant cure adhesives. They are derivatives of unsaturated acrylates which cure at room temperature without the aid of a catalyst. Films are uniform layers of adhesives that are generally rolled onto coils. Films can be supported (with reinforcing fibers), unsupported, heat-activated, or pressure-sensitive. Hot melts are generally solvent-free thermoplastics, which are solids at room temperature but soften and flow at heat activation temperature. Upon cooling the hot melt regains its structural strength. One-part adhesives are usually 99–100% solid systems. This class of adhesives includes epoxies, moisture activated silicones, and polyimides which can be waterborne or organic solvent based. Two-part epoxies and acrylics are generally cured at room temperature or accelerated with heat.
4.4 Surface Pretreatments A surface pretreatment prior to bonding is usually necessary in order to achieve long-term bond strength of aluminum substrates, although in some cases an adhesive manufacturer may state that their adhesive requires no surface pretreatment or that their adhesive is chemically incompatible with the proposed pretreatment. Many aluminum surface pretreatments have been examined to determine the best adhesive substrates for bonding. It is commonly accepted that chemically pretreating the surface yields more durable bond strength than mechanically abrading the aluminum surface. Some of the most popular chemical pretreatment systems to improve the adhesion of aluminum are degreasing, acid etching, and phosphoric acid anodizing. The adhesive manuIII-11
facturer’s recommendations for surface preparation should be followed.
4.5 Joint Design The decision to use adhesive bonding must consider joint geometry, the nature and magnitude of loading, the properties of the adhesive and the members to be joined, failure modes, and ease and reliability of manufacturing. Adapting a joint design intended for other joining methods often results in ineffective designs. The design must also consider the assembly scheme including needs for surface pretreatment, part tolerances, and fixturing. The stresses present in adhesive-bonded joints are classified based on loading: normal, shear, peel, and cleavage (Figure 4-1). Cleavage and peel conditions describe a combination of normal and shear stresses specific to these two loading conditions. Cleavage stresses are concentrated on one side of the joint, while peel loads can occur with flexible members (Kinloch (1987)). Though technically different, tensile stresses normal to the bond line are also referred to as peel stresses in the literature. Because adhesives perform best when subjected to compressive and shear loads, joint design should distribute the loads in the adhesive layer as a combination of compressive and shear stresses to avoid tensile, cleavage and peel loadings. There are four basic types of joints: angle, tee, butt, and surface or lap joints (Figure 4-2). In service, these joints may be subjected to the types of stresses mentioned in the previous paragraph. Most practical adhesive joint designs can be classified as variations of lap joints. Lap joint configurations are usually preferred because they require little or no machining. The use of overly complex configurations for low loads results in unnecessarily expensive designs. On the other hand, simple configurations are unacceptable if smooth uninterrupted surfaces are required, if high stresses are present in the bond, or if high loads must be sustained. In single lap joints that are not supported or restrained against joint rotation, bending within the joint and at the
Figure 4-2 TYPES OF JOINTS: A) ANGLE; B) TEE; C) BUTT; D) SURFACE
ends of the overlap causes locally high transverse tensile stresses in the bond. In joints that are designed to prevent or minimize joint rotation, the bond strength can exceed the full nominal strength of the members. Although adhesive bonding has benefits in joining dissimilar materials, the application imposes additional design considerations. Using materials with different moduli may result in reduced joint efficiencies. If the materials do not have similar thermal expansion coefficients, temperature changes during elevated temperature cures and in service can increase stresses in adhesive bonds and lower joint strengths (Hart-Smith (1987)). If member materials are not identical, the design should equalize the in-plane and bending stiffnesses and the materials should have similar thermal expansion coefficients. The identification of possible failure modes is crucial to effective joint design and satisfactory performance. For joints consisting of ductile isotropic materials such as aluminum alloys, four common failure modes are: 1) tensile or buckling failure of the member outside the joint area, 2) shear failure of the adhesive, 3) tensile cracking in the adhesive layer due to tensile or cleavage forces in the joint, and 4) adhesion failure at the adhesive/member interface.
Figure 4-1 TYPES OF STRESSES: A) SHEAR; B) TENSION; C) PEEL; D) CLEAVAGE III-12
Adhesion failures are least desirable because such interfacial failures typically result in low, inconsistent joint strengths. If the adhesive fails to adhere to the aluminum, this indicates incompatibility of the surface oxide of the aluminum with that particular adhesive. If the aluminum is pretreated and failure occurs at that interface between the pretreatment and the adhesive, this indicates adhesive/ pretreatment incompatibility. The adhesive properties for joint designs may be obtained from mechanical tests. Tensile properties can be obtained January 2010
using cast adhesive specimens as described in ASTM D 638 (ASTM (2009a)). Adhesive shear properties can be generated using thick adherend tests (Dreiger (1985)) or a torsion test described in ASTM E 229 (ASTM (2009b)). Properties should be obtained for temperatures throughout the range expected in service. Temperature can affect adhesive properties, ductility and toughness, which will affect joint design and performance, including stiffness and failure loads and modes. The adequacy of the design should be checked for the range of service temperatures. Summaries of technology and data are provided by Minford (1993). For critical applications in complex structures, a complete analysis of the stress components is recommended along with the identification of the potential failure modes. Nonlinear behavior of the adhesive and members should be accounted for in the most effective method of conducting such analysis. Mechanical tests to simulate typical service
January 2010
conditions of adhesive-bonded joints should be performed to verify the predicted failure location and modes.
4.6 Current Adhesive Applications Adhesives are gaining popularity as a viable structural means of joining aluminum. Today, aluminum adhesive bonding is being used in the transportation, construction, marine, aerospace, and electronic industries. Examples in each category are: • Transportation: buses, trains, and trailers; automotive seats, hoods, and air bag containers • Construction: architectural panels • Marine: boats, ships, and desalination plants • Aerospace: space vehicles, planes, and helicopters • Electronics: antennas, computer boards, and cable wires
III-13
5. Extrusion Design Aluminum can be easily extruded, unlike steel. The extrusion process consists of pushing hot aluminum through a die, likened to pushing tooth paste out of the tube. Custom shapes can be created that place the material where it is most effective. Cross sections must be constant along their length but they may be intricate. Often fabrication costs can be low-
ered by consolidating parts or incorporating assembly aids by using extrusions. Extrusions that fit within a circle up to about 30 in. in diameter are possible, but the more common ones fit within a diameter of about18 inches. The following information in this section is from the Aluminum Extrusion Manual (1998).
5.1 Replacing Fabrications with Extrusions As shown at right, several rolled and riveted structural shapes (left) can be combined into a single aluminum extrusion, thus eliminating all joining costs.
Machined and stamped sections can be replaced by aluminum sections extruded to exact size and shape.
As another example, the machining cost and weight of a framing member is reduced by redesigning the member as an extruded section.
Aluminum extrusions may also replace wood sections. They can be made lighter, stiffer, and stronger, thus eliminating steel reinforcement.
III-14
January 2010
Welded assemblies are frequently redesigned into extruded sections. Not only is cost reduced, but accuracy and strength are increased.
Because extrusions permit infinite changes in cross sectional design, they can be produced more readily to meet specific design requirements than rolled sheet sections.
Crimped tubular sections frequently permit redesign in extruded shapes, with gains in both stiffness and strength. Cost of manufacture is also reduced.
Small castings, forgings, and parts machined from bar stock may also permit redesign as an extrusion, as long as the cross section is symmetrical in at least one plane.
January 2010
III-15
5.2 Design Parameters Five major factors should be considered in the detailed development of an aluminum extrusion design: • Shape configuration • Tolerances • Surface finish • Alloy • Circumscribing circle size
put of those dies tends to approach tolerance limits. Tooling life and productivity are both improved with decreasing ratios, thus reducing cost. A solid extruded shape is any shape that is not a hollow or a semihollow. This covers a wide range including, for example, compact cross-sections with or without projections; angular or curved shapes; and those wrap-around shapes whose void area/gap2 ratios are too low for the semihollow-class.
These parameters are interrelated in their effect on the extrusion design and its application.
Shape Configuration The designer’s first priority is to satisfy a specific need, and aluminum extrusion allows you to design the shape that best meets your structural and aesthetics requirements. Since extrusion dies are relatively inexpensive, designers can afford to use several different shapes, if that’s the best way to achieve their objectives. Extrusions can be designed to aid in assembly, improve product appearance, reduce or eliminate forming and welding operations, and achieve many other purposes. Extruded shapes are described in three general categories—solid, semihollow, and hollow. Dies to produce solid shapes are the least complex. The difference between a solid shape and a semihollow shape may not be obvious at first glance. It’s easier to describe and understand all three categories by working in reverse, starting with hollow shapes. A hollow shape is simply an extruded shape which, anywhere in its cross section, completely encloses a void. The void itself may have any sort of shape, and the complete profile may include a variety of other forms; but if any part of it encloses a void, it’s classified as a “hollow.” Tube and Pipe are specific forms of hollow shapes. “Tube” is a hollow section that is long in comparison to its cross-sectional size. It is symmetrical and has uniform wall thickness except as affected by corners. It may be round or elliptical, or square, rectangular, hexagonal, or octagonal. “Extruded tube,” as the name indicates, is tube produced by hot extrusion; “drawn tube” is produced by drawing through a die. “Pipe” is a tube with certain standardized combinations of outside diameter and wall thickness. These are commonly designated by “Nominal Pipe Sizes” and by “ANSI (American National Standards Institute) Schedule Numbers.” A semihollow shape is one that partially encloses a void—for example, a circle or rectangle with a gap in one side; but a solid shape can also partially enclose a void, and the difference may not be obvious. It is defined mathematically, by comparing the area of the partially enclosed void to the size of the gap (actually, to the mathematical square of the gap size). If that ratio is larger than a certain number, the shape is classified as semihollow; if the ratio is smaller, the shape is considered a solid. The dies required to make semihollow shapes are moderately more expensive than solid shape dies, and the outIII-16
Example of a solid shape
Figure 5-1 Extruded rod is a solid shape with a round crosssection at least 0.375 in. in diameter. Extruded bar is a solid shape whose cross-section is square, rectangular, hexagonal or octagonal, and whose width between parallel faces is a least 0.375 inches. If the dimension across any of these rod- or bar-type shapes is less than 0.375 in., it is classified as wire.
Tolerances In many applications in which the extrusion will be part of an assembly of components, tolerances are critical. A designer should be aware of the standard dimensional tolerances to which extrusions are commercially produced. These tolerances generally cover such characteristics as straightness, flatness, and twist, and such cross-sectional dimensions as thickness, angles, contours and corner or fillet radii. Both standard and precision tolerances for extrusions are given in Aluminum Standards and Data, Section 11. Aluminum extrusions are often designed to minimize or eliminate the need for machining. If desired, many extrusions can be produced to the recently introduced “precision tolerances” or to closer-than-standard custom tolerances, generating cost savings in secondary operations; such savings may range from modest to very large, depending on circumstances. The designer should consider his requirements carefully and order special tolerances only where they are really needed. If extruded parts are to interlock in any manner, the designer should work with the supplier to make sure that tolerances will provide a proper fit.
Surface Finish One advantage of aluminum extrusions is the variety of ways the surface can be finished, and this offers another range of choices to the designer. January 2010
As-extruded, or “mill,” finish can range from “structural,” on which minor surface imperfections are acceptable, to “architectural,” presenting uniformly good appearance. It should be understood that under normal circumstances aluminum may be marred because it is a relatively soft metal and that special care is required if a blemish free surface is desired. Other finishes include scratch finishing, satin finishing and buffing. Aluminum can also be finished by clear or colored anodizing, or by painting or other coatings. If a product will have surfaces that are exposed in use, where normal processing marks may be objectionable, the extruders should be told which surfaces are critical. They can design a die that orients the shape to protect those surfaces during the extrusion process; they can also select packaging that will protect the product during shipment.
Alloy Selection Aluminum extrusions are made in a wide variety of alloys and tempers to meet a broad spectrum of needs. Selection is made to meet the specific requirements in strength, weldability, forming characteristics, finish, corrosion resistance, machinability, and sometimes other properties. The complete list of registered aluminum alloys is quite long, but in practice a few alloys are chosen repeatedly for extrusion because of their versatility and highly suitable characteristics. Extruders generally stock the three or four
January 2010
most frequently used alloys. When their specialized markets justify it, individual companies include in their inventories additional alloys that will vary with the needs of their major customers. Thus, a substantial variety of extrusion alloy/temper products is regularly available. The 6xxx-series of aluminum alloys is selected for nearly 75 percent of extrusion applications. Of those, alloys 6063 and 6061 are used most frequently. Alloy 6063 is used for a broad range of solid and hollow products. It is easily welded, and it has a pleasing natural finish and excellent corrosion resistance. 6063 is used in architecture and in many moderate-stress applications. Alloy 6061 is a good all-purpose extrusion alloy, combining high mechanical properties with good corrosion resistance, weldability and machining characteristics. Alloy 6061 is used in many structural applications. Many other alloys are used for extrusions to meet particular requirements. To mention a few: Characteristics
Alloys
High strength
6066, 6070, 6082, 7005
High corrosion resistance
1100, 3003
High electrical conductivity
6101
The designer should consult alloy and temper tables and discuss specific needs with the extrusion supplier.
III-17
Circumscribing Circle Size One measurement of the size of an extrusion is the diameter of the smallest circle that will entirely enclose its cross-section—its “circumscribing circle.” This dimension is one factor in the economics of an extrusion. In gen-
eral, extrusions are most economical when they fit within medium-sized circumscribing circles: that is, one with a diameter between 1 and 10 inches. The example shown in Figure 5-2 would be classified as a 3 to 4 in. circle size shape.
Figure 5-2
III-18
January 2010
5.3 Design Guidelines Good Extrusion Design Practices At this stage in the development of an extruded product, the designer has determined its functional shape and size, and considered appropriate tolerances, surface finishes and alloys. Before proceeding, it makes sense to review the extruder’s available standard shapes. It may be possible to adapt a standard shape to the needs of the product, with little or no modification. If a standard shape is not readily adaptable, the design can be completed as a custom shape perfectly suited to the requirements of the product. Here are a few tips on good practices in custom-designing aluminum extrusions:
Specify the Most Appropriate Metal Thicknesses Specify metal thicknesses that are just heavy enough to meet your structural requirements. Even in low stress areas, however, keep sufficient thickness to avoid risking distortion or damage. Some shapes tend to invite distortion during the extrusion process (such as an asymmetric profile or thin details at the end of a long flange). Such tendencies exert more influence on thin-walled shapes than on those with normal metal thickness.
For example, a U-shaped channel in an extrusion corresponds to a solid “tongue” in the die, attached at only one end. Flexibility in this tongue can alter the aperture slightly under the pressure of extrusion; the deeper you make the channel, the longer you make the tongue and the more difficult it becomes to regulate the extruded dimensions. On the other hand, rounding corners at the base and tip of the tongue can ease metal flow and so help to keep the extruded dimensions more uniform. Even corners rounded to only ⅙₄ in. radius can facilitate extruding. Visualize the shape of the die that must produce your design, and try to minimize shapes that would weaken the die or impede metal flow.
Use Metal Dimensions for Best Tolerance Dimensions measured across solid metal are easier to produce to closer tolerances than those measured across a gap or angle (see Figure 5-3). So rely on metal dimensions as much as possible when designing close-fitted mating parts or other shapes requiring closer tolerances. Standard industry dimensional tolerances are entirely adequate for many applications, but special tolerances can be specified if necessary.
Keep Metal Thickness as Uniform As Possible Extrusion allows you to put extra metal where it is needed— in high-stress areas, for example—and still save material by using normal dimensions elsewhere in the same piece. Adjacent wall thickness ratios of less than 2-to-1 are extruded without difficulty. However, large contrasts between thick and thin areas may create uneven conditions during extrusion. It is best to maintain near uniform metal thickness throughout a shape if possible. When a design combines thick and thin dimensions, streamline the transitions with a radius (a curve, rather than a sharp angle) at junctions where the thickness changes sharply. Rounded corners ease the flow of metal.
An Open Space Dimension is more difficult to hold to close tolerances.
Visualize the Die and the Metal Flow Remember what an extrusion die does: while it lets metal flow through its shaped aperture, it must hold back metal all around that aperture against great force. When you design a shape for extrusion, you are simultaneously designing a die aperture and you must take extrusion forces and metal flow into account.
January 2010
A Metal Dimension can be extruded to close tolerances.
Figure 5-3
III-19
Smooth All Transitions Transitions should be streamlined by a generous radius at any thick-thin junction.
Instead of This
Consider This
Keep Wall Thickness Uniform The preceding shape can be further improved by maintaining uniform wall thickness. In addition to using more metal, thick-thin junctions give rise to distortion, die breakage or surface defects on the extrusion. Ribs Help Straightening Operation Wide, thin sections can be hard to straighten after extrusion. Ribs help to reduce twisting and to improve flatness. Symmetry Preferred in Semi-Hollow Areas When designing, visualize the die and tongue that will be necessary to produce a semi-hollow shape. By keeping the void symmetrical you lessen the chances that the die tongue may break.
Figure 5-4
III-20
January 2010
5.4 Design for Assembly Aluminum extrusions can be designed for joining by a wide variety of assembly methods such as riveting, bolting, welding, brazing, soldering and adhesive bonding. They can also be designed to fit, hook or snap together with mating parts. Hinges or slides can often by “designedin” as integral parts of extrusions, eliminating the need for additional assembly and moving parts. Four types of extruded joints are discussed in this section: • Nesting Joints • Interlocking Joints • Snap-Fit Joints • Screw Slots
Nesting Joints Nesting joints, which include lap joints and tongue-andgroove joints, have mating elements that are shaped to be assembled with little or no self-locking action. They serve primarily to align adjoining parts, and they usually depend on rivets, bolts, adhesives, confinement within a rigid frame, or other fasteners to hold them together. Lap joints, shown in Figure 5-5, are the simplest nesting joints.
Interlocking Joints The interlocking joint is, in effect, a modified tongueand-groove. But instead of being straight, the two mating elements are curved and so cannot be assembled or (more to the point) disassembled by simple straight-line motion. They are assembled by a rotating motion and will not separate without a corresponding counter-rotation. As long as the parts are held in their assembled position, they strongly resist separation and misalignment in both the horizontal and the vertical directions. The amount of rotation required for interlocking assembly depends on the geometry of the design. It can be made more or less than 45°, as long as the design allows enough clearance for the required rotation. Interlocking joints can be secured in at least five ways, all based on preventing counter-rotation. • Fastening the elements to structural cross-members. • Restraining the assembly within a rigid frame. • Restraining the assembly with channel end-closures. • Fastening the joint with rivets, welds, adhesives or other devices. • Providing a folding, locking flange as shown in Figure 5-6.
January 2010
Figure 5-5
III-21
Snap-Fit Joints
Screw Slots
A “snap-fit” or “snap-lock” joint (see Figure 5-7) is one which is self-locking and requires no additional fasteners to hold the joint together. The mating parts of a snap-fit joint exert a cam action on each other, flexing until one part slips past a raised lip on the other part. Once past this lip, the flexed parts snap back to their normal shape and the lip prevents them from separating. After it is snapped together, this joint cannot be disassembled unintentionally. This joint’s strength can be increased by applying adhesive to the mating surfaces before assembly. Even short lengths of an adhesively bonded, snap-fit joint cannot be easily slid apart. Precise dimensions are critical in a snap-fit joint. Experienced extrusion designers who are fully conversant with snap-fit production requirements can determine the precise final dimensions.
Screw slots are often used to facilitate the assembly of aluminum extrusions. Standard screw slots are illustrated in Figure 5-8 and should always be used with self tapping screws. The screw slot should be designed so that the area of the void and the metal thickness surrounding it is symmetrical about the center line of the gap. Sheet metal type screws are not recommended since their thread projects to the end of the screw and thereby can “walk” through the slot opening.
Self Tapping Screw Type F NF
Screw OD (in.)
A DIA. (in.)
4–401
4–481
0.120
0.099 ± 0.006
6–32
1
6–401
0.138
0.120 ± 0.006
8–32
8–36
0.164
0.147 ± 0.007
NC
Figure 5-6
10–24
10–32
0.190
0.169 ± 0.007
12–24
12–28
0.216
0.190 ± 0.007
¼ × 20
¼ × 28
0.250
0.228 ± 0.007
Not recommended for incorporation on inside wall of hollow or semihollow shapes. 2The recommended location for screw slots on the inside of hollow or semihollow shapes is at the corners. When not located at corners dimension “B” must be at least 0.250 in. 1
Figure 5-7
III-22
Figure 5-8
January 2010
6. Preventing Corrosion A great deal of technology and experience exists for successful prevention of corrosion in assemblies and structures. The following information has been adapted from Hatch (1984). Proper selection/application of the following measures can be used to prevent aluminum corrosion: • Alloy and temper selection • Design • Joints • Inhibitors • Protective coatings • Cathodic protection Alloy and temper selection: Alloys of the 1xxx, 3xxx, 5xxx, and 6xxx series generally have very good corrosion resistance in natural environments and can often be used without corrosion protection. Temper selection for the 1xxx, 3xxx, and 6xxx series alloys and for the 5xxx series alloys containing up to 3% magnesium (e.g. 5005, 5050, 5052, and 5454) may be based on factors other than corrosion. For 5xxx series sheet and plate alloys containing more than 3% magnesium (e.g. 5083, 5086, and 5456) for applications with service temperatures exceeding 150°F or in marine environments, the temper should be limited to H116 or H321 and material should comply with ASTM B 928 to guard against intergranular and exfoliation corrosion. Alloys of the 2xxx and 7xxx series alloys have relatively poor corrosion resistance and require corrosion protection. Temper selection for the 2xxx and 7xxx series alloys can significantly affect exfoliation and stress corrosion resistance. For these alloys, consideration should also be given to stress corrosion cracking (SCC). SCC can occur when residual or assembly stresses occur in the through-thickness or short transverse direction. This can be minimized by considering temper selection, residual stresses from fabrication (e.g. forming, machining, and thermal treatments), and fit up details. Design: Factors that may affect corrosion resistance can be more cost-effectively considered during the design phase rather than after the design is finalized: • Avoid contacts with dissimilar metals (galvanic corrosion prevention discussed below). • Avoid crevices, especially at joints (crevice corrosion prevention discussed below). • Avoid skip welding by using continuous welding. • Avoid standing fluid and poultice catchments. • Avoid placing absorbent materials, such as open-cell gaskets, insulation, and soundproofing, against aluminum. • Avoid direct impingement by fluid streams, especially sharp pipe bends. • Avoid heat transfer hot spots. • Avoid corrosive conditions when locating parts and joints. • Avoid sharp edges when coating will be used. January 2010
Joints: A key area for corrosion prevention is joints. Joints may involve aluminum and other metals. Galvanic corrosion can occur when aluminum is joined to other metals and the joint is connected by a conductive fluid. Joints designed so that they remain dry in service or where the dissimilar metals are not electrically connected, even by a remote path, will be free from galvanic corrosion. A common tool for predicting which metal will corrode (anode) in a given couple is the galvanic series, which is environment-specific (see Table 6-1 for an example in sodium chloride solution). In Table 6-1 the metal in a galvanic couple that is toward the active end of the galvanic series will corrode, and the other metal in the couple which is toward the noble end of the series will not corrode. The galvanic series is useful only as a predictive tool as to location of corrosion in a galvanic couple, not corrosion rate. However, selection of couple members that are close together in the galvanic series minimizes galvanic corrosion. Aluminum can be coupled to magnesium, zinc, cadmium, and passive stainless steel in most environments without galvanic corrosion. In most other galvanic couples aluminum will experience galvanic corrosion. Where dissimilar metals must be joined, creating an undesirable galvanic couple, several steps can be taken to minimize corrosion. The exposed area of the more noble or cathodic metal should be minimized by design and by application of protective coatings (e.g. paint, gasket, or tape). At bolted or riveted galvanic joints (e.g. aluminum to steel) the fasteners (the smaller exposed surface area) should be the more noble material, such as steel or 3xx series stainless steel rather than aluminum. If using steel fasteners, a further required step is to coat the fasteners with a zinc (galvanizing) or other suitable coating. Where galvanic couples have only a few points of electrical contact, it may be possible to control corrosion by electrical insulation. Insulation can be effective only when all points of electrical contact are broken. Insulation can be achieved by inserting nonmetallic, non-wicking bushings, gaskets, sleeves, or tapes into joints. Such insulation is difficult to achieve in large, complex structures where remote electrical paths may exist. Crevices are inevitable in structures. When crevices trap foreign matter, accelerated corrosion may result. Often joints can be located or oriented to minimize moisture ingress and retention. Adhesives, sealants, and nonabsorbent gaskets can prevent the ingress of moisture into crevices. Continuous welds are more desirable than intermittent welds because they leave no crevices. A type of crevice corrosion known as poultice corrosion can occur under foreign materials, such as mud, paper, or cloth. Poultice corrosion can often be minimized by avoiding catchments and pockets during design of a structure. Inhibitors: In fluid-carrying systems where piping of aluminum and other metals are joined, a thick-walled, replaceable aluminum nipple should be used at the joint. In closed III-23
Table 6-1 GALVANIC SERIES IN SODIUM CHLORIDE SOLUTION (similar to sea water) Magnesium Zinc Aluminum alloy 7072 (used in Alclad products) 5xxx aluminum alloys 7xxx structural aluminum alloys 1xxx, 3xxx, 6xxx aluminum alloys Cadmium 2xxx aluminum alloys Iron and steel Lead Tin Brass Copper Stainless steel (3xx, passive) Nickel
III-24
Anode
Cathode
loop, mixed metal fluid-carrying systems, such as automotive cooling systems, it may be possible to control galvanic corrosion with a mixed metal corrosion inhibitor. Mixed metal fluid-carrying systems that include aluminum and cannot be treated with inhibitors should not contain copper. Protective Coatings: When surface treatments such as anodizing, organic coating, or plating are used on aluminum to provide consistent appearance or improve corrosion resistance, the quality of the treatment is extremely important. If flaws or points of damage occur which expose the substrate aluminum surface, accelerated localized pitting corrosion may result. See Part I and Part II Section M.7 for additional information on contact with dissimilar materials. Cathodic Protection: For aluminum structures that are buried or immersed in aqueous environments, corrosion may be controlled by application of the electrochemical process known as cathodic protection.
January 2010
7. Fire Protection Aluminum alloys are non-combustible when tested in accordance with ASTM E 136. The behavior of aluminum and steel members exposed to fire are compared below.
Kaufman and Kasser (1963) tested fire protection for aluminum members. The criteria for establishing the fire protection for aluminum were:
1. Both aluminum and steel members are noncombustible. 2. The cross sectional areas of aluminum members are usually about 40% larger than those of steel. 3. The thermal conductivity of aluminum is about 2.7 times that of steel. 4. Aluminum’s strength degrades at much lower temperatures than that of steel.
1. To ensure that strength during a fire will at least equal the allowable stresses at room temperature, the aluminum temperature should be limited to 500°F. 2. To ensure that there will be no substantial change in properties after a fire, the aluminum temperature should be limited to 375°F.
These issues affect the relative performance of the two materials in a fire. Aluminum parts exposed to fire would be expected to reach a lower temperature than steel, but aluminum’s strength relative to that at room temperature is more degraded compared to that for steel. Aluminum members thus need more insulation than steel members to resist the effects of fire.
Light weight vermiculite plaster was used in the tests, and specimens were as indicated on Figure 7-1. The relative thicknesses of protection required for various periods of time are shown below. Part I Appendix 4 and Eurocode 9, Part 1-2 address aluminum structural design for fire conditions.
RELATIVE THICKNESS OF VERMICULITE
REQUIRED FOR FIRE PROTECTION OF STRUCTURAL ALUMINUM MEMBERS Fire Protection Period (hours)
Ratio of Aluminum Member’s Insulation Thickness to Steel Member’s Insulation Thickness
1
1.7
2
1.9
3
1.8
4
1.7
Numbers designate materials as follows: (1) 8WF × 10.72 column (2) Vermiculite plaster (3) Lath (4) Keystone key corner beads
Figure 7-1 SPECIMENS FOR FIRE PROTECTION TESTS
January 2010
III-25
8. Sustainability 8.1 Reflectance and Emittance In warm climates, the more roofs reflect and radiate the sun’s radiation, the more energy they save by reducing buildings’ cooling requirements. Solar reflectance, also called albedo, measures a material’s ability to reflect sunlight—including visible, infrared, and ultraviolet wavelengths—on a scale of 0 to 1 and can be expressed as a decimal fraction or a percentage. Thermal emittance is the fraction of energy a material radiates away after it is absorbed. Emittance is the ability to release absorbed heat and is also expressed as a decimal fraction or a percentage. Reflectance is determined using ASTM E 1918 or C 1549; emittance is determined according to ASTM E 408 or C 1371. Cooling energy requirements are significantly reduced by roofing materials with high reflectance and emittance. For prepainted metal roofing, the substrate has little or no influence on the exterior surface reflectance and emittance. The emittance of painted metal is about 0.8 to 0.9. The reflectance is a function of paint color and type. Reflectance and emittance of bare aluminum is affected by surface roughness, oxides, and cleanliness. Typical total
III-26
solar reflectance is 0.6 to 0.8. Mill finish aluminum can have very low emittance (0.02 to 0.10), although this increases slightly as natural oxides form. Aluminum is often anodized to create a durable layer of aluminum oxide that is much thicker than that which occurs naturally. Anodized aluminum has significantly higher emittance (0.6 to 0.9).
8.2 Recycling Aluminum can be recycled indefinitely without loss of properties. Aluminum is 100% recyclable, and recycling aluminum saves approximately 95% of the energy required to produce aluminum from bauxite. Using recycled aluminum instead of raw materials reduces air and water pollution by about 95%. A 2008 survey of aluminum producers indicated that the total recycled content of domestically produced flat rolled products for the building and construction market was approximately 85%. On average, 60% of the total product content was from post-consumer sources. To determine the recycled content of specific aluminum products, consult the supplier.
January 2010
9. References AAMA (1990), Structural Performance, Poured and Debridged Framing Systems, TIR-A8-90, Schaumberg, IL. Aluminum Association (1987), The Aluminum Association Position on Fracture Toughness Requirements and Quality Control Testing 1987, T-5, Washington, DC. Aluminum Extruders Council and the Aluminum Association (1998), The Aluminum Extrusion Manual, Wauconda, IL. ASTM (2009a), Vol. 08.01, “Plastics,” American Society for Testing and Materials, West Conshohocken, PA, 2009. ASTM (2009b), Vol. 15.06, “Adhesives,” American Society for Testing and Materials, West Conshohocken, PA, 2009. D.A.T.A., Inc. (1986), Adhesives, 4th Edition. Drieger, R. B., “Analyzing Joint Stresses Using an Extenso meter,” Adhesive Age, pp 26–28, October, 1985. Hart-Smith, A. J., “Design of Adhesively Bonded Joints,” Joining Fibre-Reinforced Plastics, F. L. Mathews, editor, Elsevier Applied Science Publishing, New York, NY, 1987. Hatch, John E., ed., Aluminum—Properties and Physical Metallurgy, American Society for Metals, 1984, pp. 300– 309.
January 2010
Kaufman, J. G. and Kasser, R. C., “Fire Protection for Aluminum Alloy Structural Shapes,” Civil Engineering, March, 1963. Kinloch, A. J., Adhesion and Adhesives, Science and Technology, Chapman and Hall, New York, NY, 1987. Menzemer, Craig C., (1992), Fatigue Behavior of Welded Aluminum Structures, Dissertation in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Lehigh University, Bethlehem, PA. Metal Construction Association (2004), Primer on Diaphragm Design, Glenview, IL. Minford, J. Dean (1993), Handbook of Aluminum Bonding Technology and Data, Marcel Dekker, Inc., New York. Sharp, Maurice L., Behavior and Design of Aluminum Structures, McGraw-Hill Inc., New York, NY, 1993. Shields, J., Adhesives Handbook, CRC Press, 1970. Sooi, Took Kowng, “Behavior of Component Elements of Aluminum Members,” Research Report No. 93-1, Teoman Peköz, Project Director, Cornell University, 1993. Thrall, Edward W. and Shannon, Raymond W., Adhesive Bonding of Aluminum Alloys, Marcel Dekkar, New York, NY, 1984.
III-27
Aluminum Design Manual
PART IV Material Properties
IV Material Properties TABLE OF CONTENTS 1 .
General Characteristics of Aluminum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2 .
Aluminum Metallurgy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7
3. Wrought Aluminum and Aluminum Alloy Designation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.1 Aluminum. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Aluminum Alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 Experimental Alloys. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 National Variations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4. Cast Aluminum and Aluminum Alloy Designation System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.1 Aluminum Castings and Ingot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 Aluminum Alloy Castings and Ingot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.3 Experimental Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 5 .
Effect of Alloying Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
6. Temper Designation System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.1 Basic Temper Designation System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.2 Subdivisions of Basic Tempers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.2.1 Subdivisions of H temper: Strain-hardened. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 6.2.2 Subdivisions of T Temper: Thermally Treated . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 6.3 Variations of O Temper: Annealed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Table 1 Comparative Characteristics and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Table 2 Foreign Alloy Designations and Similar AA Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Table 3 Mechanical Property Limits for Commonly Used Sand Casting Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Table 4 Mechanical Property Limits for Commonly Used Permanent Mold Casting Alloys . . . . . . . . . . . . . . . . . . . . . . . . 23 Table 5 Mechanical Property Limits of Fastener Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Table 5M Mechanical Property Limits of Fastener Alloys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Table 6 Typical Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Table 6M Typical Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Table 7 Typical Physical Properties—Thermal and Electrical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Table 7M Typical Physical Properties—Thermal and Electrical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 Table 8 Typical Physical Properties—Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Table 9 Typical Tensile Properties at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Table 9M Typical Tensile Properties at Various Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Information in Part IV is excerpted from Aluminum Standards and Data 2009 and Aluminum Standards and Data 2009 Metric SI.
January 2010
IV-3
1. General Characteristics of Aluminum A unique combination of properties makes aluminum one of our most versatile engineering and construction materials. A mere recital of its characteristics is impressive. It is light in mass, yet some of its alloys have strengths greater than that of structural steel. It has high resistance to corrosion under the majority of service conditions, and no colored salts are formed to stain adjacent surfaces or discolor products with which it comes into contact, such as fabrics in the textile industry and solutions in chemical equipment. It has no toxic reaction. It has good electrical and thermal conductivities and high reflectivity to both heat and light. The metal can easily be worked into any form and readily accepts a wide variety of surface finishes. Lightness is one of aluminum’s most useful characteristics. The specific gravity is about 2.7. The mass (“weight”) of aluminum is roughly 35 percent that of iron and 30 percent that of copper. Commercially pure aluminum has a tensile strength of about 13,000 pounds per square inch. Thus its usefulness as a structural material in this form is somewhat limited. By working the metal, as by cold rolling, its strength can be approximately doubled. Much larger increases in strength can be obtained by alloying aluminum with small percentages of one or more other elements such as manganese, silicon, copper, magnesium or zinc. Like pure aluminum, the alloys are also made stronger by cold working. Some of the alloys are further strengthened and hardened by heat treatments so that today aluminum alloys having tensile strengths approaching 100,000 pounds per square inch are available. A wide variety of mechanical characteristics, or tempers, is available in aluminum alloys through various combina tions of cold work and heat treatment. In specifying the temper for any given product, the fabricating process and the amount of cold work to which it will subject the metal should be kept in mind. In other words, the temper specified should be such that the amount of cold work the metal will receive during fabrication will develop the desired characteristics in the finished products. Aluminum and its alloys lose part of their strength at elevated temperatures, although some alloys retain good strength at temperatures from 400˚F to 500˚F. At subzero temperatures, however, their strength increases without loss of ductility, so that aluminum is a particularly useful metal for low-temperature applications. When aluminum surfaces are exposed to the atmosphere, a thin invisible oxide skin forms immediately, which protects the metal from further oxidation. This self-protecting characteristic gives aluminum its high resistance to corrosion. Unless exposed to some substance or condition that destroys this protective oxide coating, the metal remains fully protected against corrosion. Aluminum is highly resistant to weathering, even in industrial atmospheres that often corJanuary 2010
rode other metals. It is also corrosion resistant to many acids. Alkalis are among the few substances that attack the oxide skin and therefore are corrosive to aluminum. Although the metal can safely be used in the presence of certain mild alkalis with the aid of inhibitors, in general, direct contact with alkaline substances should be avoided. Some alloys are less resistant to corrosion than others, particularly certain high-strength alloys. Such alloys in some forms can be effectively protected from the majority of corrosive influences, however, by cladding the exposed surface or surfaces with a thin layer of either pure aluminum or one of the more highly corrosion-resistant alloys. A word of caution should be mentioned in connection with the corrosion-resistant characteristics of aluminum. Direct contacts with certain other metals should be avoided in the presence of an electrolyte; otherwise galvanic corrosion of the aluminum may take place in the vicinity of the contact area. Where other metals must be fastened to aluminum, the use of a bituminous paint coating or insulating tape is recommended. The fact that aluminum is nontoxic was discovered in the early days of the industry. It is this characteristic that permits the metal to be used in cooking utensils without any harmful effect on the body, and today we find also a great deal of aluminum equipment in use by food process ing industries. The same characteristic permits aluminum foil wrapping to be used safely in direct contact with food products. Aluminum is one of the two common metals having an electrical conductivity high enough for use as an electric conductor. The conductivity of electric conductor grade (1350) is about 62 percent that of the International Annealed Copper Standard. Because aluminum has less than one-third the specific gravity of copper, however, a pound of aluminum will go about twice as far as a pound of copper when used for this purpose. Alloying lowers the conductivity somewhat, so that wherever possible alloy 1350 is used in electric conductor applications. The high thermal conductivity of aluminum came prom inently into play in the very first large-scale commercial application of the metal in cooking utensils. This character istic is important wherever the transfer of thermal energy from one medium to another is involved, either heating or cooling. Thus aluminum heat exchangers are commonly used in the food, chemical, petroleum, aircraft and other industries. Aluminum is also an excellent reflector of radiant energy through the entire range of wavelengths, from ultraviolet, through the visible spectrum to infrared and heat waves, as well as electromagnetic waves of radio and radar. Aluminum has a light reflectivity of over 80 percent, which has led to its wide use in lighting fixtures. Aluminum roofing reflects a high percentage of the sun’s heat, so that buildings roofed with this material are cooler in summer. IV-5
The ease with which aluminum may be fabricated into any form is one of its most important assets. Often it can compete successfully with cheaper materials having a lower degree of workability. The metal can be cast by any method known to foundrymen; it can be rolled to any desired thickness down to foil thinner than paper; aluminum sheet can be stamped, drawn, spun or roll-formed. The metal also may be hammered or forged. Aluminum wire, drawn from rolled rod, may be stranded into cable of any desired size and type. There is almost no limit to the different profiles (shapes) in which the metal may be extruded. The ease and speed with which aluminum may be machined is one of the important factors contributing to the low cost of finished aluminum parts. The metal may be turned, milled, bored, or machined in other manners at the maximum speeds of which the majority of machines are capable. Another advantage of its flexible machining characteristics is that aluminum rod and bar may readily be employed in the highspeed manufacture of parts by automatic screw machines. Almost any method of joining is applicable to aluminum: riveting, welding, brazing or soldering. A wide variety of mechanical aluminum fasteners simplifies the assembly of many products. Adhesive bonding of aluminum parts is widely employed, particularly in joining aircraft components. For the majority of applications, aluminum needs no protective coating. Mechanical finishes such as polishing, sand blasting or wire brushing meet the majority of needs. In many instances, the surface finish supplied is entirely adequate without further finishing. Where the plain aluminum surface does not suffice, or where additional protection is required, any of a wide variety of surface finishes may be applied. Chemical, electrochemical and paint finishes are all used. Many colors are available in both chemical and electrochemical finishes. If paint, lacquer or enamel is used, any color possible with these finishes may be applied. Vitreous enamels have been developed for aluminum, and the metal may also be electroplated. Aluminum sheet, because of its superior corrosion resis tance and smooth continuous surface, is an excellent base for the high quality paints used in producing painted sheet. The chemical pretreatment plus the application of high quality thermally cured paint assures a finish that will exhibit no cracking, blistering, or peeling. Accidental damage to products made of painted aluminum sheet will not result in unsightly rust areas or streaks. Experience has shown that paint in the quality used for this product, properly formulated, applied and cured, will show little change in color or loss of gloss after one year’s service in the adverse climatic conditions of south-central Florida. Highly industrialized areas may cause some color change due to atmospheric contaminants.
IV-6
Proper maintenance can extend the service life considerably—even the finest automobiles require occasional washing and polishing if they are to retain their original appearance. Even after many years of service most advantages of the painted sheet remain. It can be repainted with any good grade of house paint with no danger of cracking or peeling, such as is often experienced when paint is applied to other types of base materials. Painted sheet and the products made from it should be handled with care to avoid damage to the paint film. Repair of large damaged areas is not recommended, but for repair of small areas air drying touch-up paint intended for brush application is available from paint suppliers. Your painted sheet supplier should be contacted for precise information. This touch-up paint cannot be expected to exhibit the same weathering and other characteristics as the original painted sheet, and touched-up areas will present appearance differences after weather exposure. For this reason, use of touch-up paint should be held to a minimum. Many types of paint systems are used, and it is difficult to establish reasonable and meaningful standards for all of them. Specific applications require consideration of life expectancy, forming requirements and methods, economics, and so forth. Paint systems generally in use exhibit general characteristics as shown on Aluminum Standards and Data 2009 pages 7-31 to 7-33, but for specific applications consult the painted sheet supplier. These are the characteristics that give aluminum its extreme versatility. In the majority of applications, two or more of these characteristics come prominently into play— for example, light weight combined with strength in airplanes, railroad cars, trucks and other transportation equipment. High resistance to corrosion and high thermal conductivity are important in equipment for the chemical and petroleum industries; these properties combine with nontoxicity for food processing equipment. Attractive appearance together with high resistance to weathering and low maintenance requirements have led to extensive use in buildings of all types. High reflectivity, excellent weathering characteristics, and light weight are all important in roofing materials. Light weight contributes to low handling and shipping costs, whatever the application. Many applications require the extreme versatility that only aluminum has. Almost daily its unique combination of properties is being put to work in new ways. The metal now serves as a basic raw material for more than 20,000 businesses scattered throughout the country.
January 2010
2. Aluminum Metallurgy In high-purity form aluminum is soft and ductile. Most commercial uses, however, require greater strength than pure aluminum affords. This is achieved in aluminum first by the addition of other elements to produce various alloys, which singly or in combination impart strength to the metal. Further strengthening is possible by means that classify the alloys roughly into two categories, non-heat-treatable and heat-treatable. Non-heat-treatable alloys—The initial strength of alloys in this group depends upon the hardening effect of elements such as manganese, silicon, iron and magnesium, singly or in various combinations. The non-heat-treatable alloys are usually designated, therefore, in the 1xxx, 3xxx, 4xxx, or 5xxx series. Since these alloys are work-hardenable, further strengthening is made possible by various degrees of cold working, denoted by the “H” series of tempers. Alloys containing appreciable amounts of magnesium when supplied in strain-hardened tempers are usually given a final elevatedtemperature treatment called stabilizing to ensure stability of properties. Heat-treatable alloys—The initial strength of alloys in this group is enhanced by the addition of alloying elements such as copper, magnesium, zinc, and silicon. Since these elements singly or in various combinations show increasing solid solubility in aluminum with increasing temperature, it is possible to subject them to thermal treatments that will impart pronounced strengthening. The first step, called heat treatment or solution heat treatment, is an elevated-temperature process designed to put the soluble element or elements in solid solution. This is followed by rapid quenching, usually in water, which momentarily “freezes” the structure and for a short time renders the alloy very workable. It is at this stage that some fabricators retain this more workable structure by storing the alloys at below freezing temperatures until they are ready to form them. At room or elevated temperatures the
January 2010
alloys are not stable after quenching, however, and precipitation of the constituents from the super-saturated solution begins. After a period of several days at room temperature, termed aging or room-temperature precipitation, the alloy is considerably stronger. Many alloys approach a stable condition at room temperature, but some alloys, particularly those containing magnesium and silicon or magnesium and zinc, continue to age-harden for long periods of time at room temperature. By heating for a controlled time at slightly elevated temperatures, even further strengthening is possible and properties are stabilized. This process is called artificial aging or precipitation hardening. By the proper combination of solution heat treatment, quenching, cold working and artificial aging, the highest strengths are obtained. Clad alloys—The heat-treatable alloys in which cop per or zinc are major alloying constituents are less resistant to corrosive attack than the majority of non-heat-treatable alloys. To increase the corrosion resistance of these alloys in sheet and plate form, they are often clad with high-purity aluminum, a low magnesium-silicon alloy, or an alloy containing 1 percent zinc. The cladding, usually from 2½ percent to 5 percent of the total thickness on each side, not only protects the composite due to its own inherently excellent corrosion resistance but also exerts a galvanic effect, which further protects the core material. Special composites may be obtained such as clad nonheat-treatable alloys for extra corrosion protection, for brazing purposes, or for special surface finishes. Some alloys in wire and tubular form are clad for similar reasons, and on an experimental basis extrusions also have been clad. Annealing characteristics—All wrought aluminum alloys are available in annealed form. In addition, it may be desirable to anneal an alloy from any other initial temper, after working, or between successive stages of working such as in deep drawing.
IV-7
3. Wrought Aluminum and Aluminum Alloy Designation System Q A system of four-digit numerical designations is used to identify wrought aluminum and wrought aluminum alloys. The first digit indicates the alloy group as follows: Aluminum, 99.00 percent and greater . . . . . . . . . . . . . . . . Aluminum alloys grouped by major alloying elements W E R Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manganese . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnesium and silicon . . . . . . . . . . . . . . . . . . . . . . . . . . Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unused series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1xxx 2xxx 3xxx 4xxx 5xxx 6xxx 7xxx 8xxx 9xxx
The designation assigned shall be in the 1xxx group whenever the minimum aluminum content is specified as 99.00 percent or higher. The alloy designation in the 2xxx through 8xxx groups is determined by the alloying element (Mg2Si for 6xxx alloys) present in the greatest mean percentage, except in cases in which the alloy being registered qualifies as a modification or national variation of a previously registered alloy. If the greatest mean percentage is common to more than one alloying element, choice of group will be in order of group sequence Cu, Mn, Si, Mg, Mg2Si, Zn or others. The last two digits identify the aluminum alloy or indicate the aluminum purity. The second digit indicates modifica tions of the original alloy or impurity limits.
Q Chemical composition limits and designations conforming to this standard for wrought aluminum and wrought aluminum alloys, and aluminum and aluminum alloy castings and foundry ingot may be registered with The Aluminum Association provided: (1) the aluminum or aluminum alloy is offered for sale, (2) the complete chemical composition limits are registered, and (3) the composition is significantly different from that of any aluminum or aluminum alloy for which a numerical designation already has been assigned. W For codification purposes an alloying element is any element that is intentionally added for any purpose other than grain refinement and for which minimum and maximum limits are specified. E Standard limits for alloying elements and impurities are expressed to the following places: Less than .001 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.000X .001 but less than .01 percent . . . . . . . . . . . . . . . . . . . . . . . 0.00X .01 but less than .10 percent Unalloyed aluminum made by a refining process . . . . . . 0.0XX Alloys and unalloyed aluminum not made by a refining process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.0X .10 through .55 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.XX (It is customary to express limits of 0.30 percent through 0.55 percent as 0.X0 or 0.X5) Over .55 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.X, X.X, etc. (except that combined Si + Fe limits for 1xxx designations must be expressed as 0.XX or 1.XX) R Standard limits for alloying elements and impurities are expressed in the following sequence: Silicon; Iron; Copper; Manganese; Magnesium; Chromium; Nickel; Zinc; Titanium (see Note 1); Other (see Note 2) Elements, Each; Other (see Note 2) Elements, Total; Aluminum (see Note 3).
IV-8
3.1 Aluminum In the 1xxx group for minimum aluminum purities of 99.00 percent and greater, the last two of the four digits in the designation indicate the minimum aluminum percent age.T These digits are the same as the two digits to the right of the decimal point in the minimum aluminum percentage when it is expressed to the nearest 0.01 percent. The second digit in the designation indicates modifications in impurity limits or alloying elements. If the second digit in the designation is zero, it indicates unalloyed aluminum having natural impurity limits; integers 1 through 9, which are assigned consecutively as needed, indicate special control of one or more individual impurities or alloying elements.
3.2 Aluminum Alloys In the 2xxx through 8xxx alloy groups the last two of the four digits in the designation have no special significance but serve only to identify the different aluminum alloys in the group. The second digit in the alloy designation indicates alloy modifications. If the second digit in the designation is zero, it indicates the original alloy; integers 1 through 9, which are assigned consecutively, indicate alloy modifications. A modification of the original alloy is limited to any one or a combination of the following: (a) Change of not more than the following amounts in arithmetic mean of the limits for an individual alloying element or combination of elements expressed as an alloying element or both.
Note 1—Additional specified elements having limits are inserted in alphabetical order according to their chemical symbols between Titanium and Other Elements, Each, or are listed in footnotes. Note 2—“Other” includes listed elements for which no specific limit is shown as well as unlisted metallic elements. The producer may analyze samples for trace elements not specified in the registration or specification. However, such analysis is not required and may not cover all metallic “other” elements. Should any analysis by the producer or the purchaser establish that an “other” element exceeds the limit of “Each” or that the aggregate of several “other” elements exceeds the limit of “Total”, the material shall be considered non-conforming. Note 3—Aluminum is specified as minimum for unalloyed aluminum, and as a remainder for aluminum alloys. T The aluminum content for unalloyed aluminum made by a refining process is the difference between 100.00 percent and the sum of all other metallic elements plus silicon present in amounts of 0.0010 percent or more, each expressed to the third decimal before determining the sum, which is rounded to the second decimal before subtracting; for unalloyed aluminum not made by a refining process it is the difference between 100.00 percent and the sum of all other analyzed metallic elements plus silicon present in amounts of 0.010 percent or more, each expressed to the second decimal before determining the sum. For unalloyed aluminum made by a refining process, when the specified maximum limit is 0.0XX, an observed value or a calculated value greater than 0.0005 but less than 0.0010% is rounded off and shown as “less than 0.001”; for alloys and unalloyed aluminum not made by a refining process, when the specified maximum limit is 0.XX, an observed value or a calculated value greater than 0.005 but less than 0.010% is rounded off and shown as “less than 0.01”.
January 2010
Arithmetic Mean of Limits for Alloying Elements in Original Alloy
3.4 National Variations Maximum Change
Up thru 1.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 1.0 thru 2.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 2.0 thru 3.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 3.0 thru 4.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 4.0 thru 5.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 5.0 thru 6.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 6.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.15 0.20 0.25 0.30 0.35 0.40 0.50
To determine compliance when maximum and mini mum limits are specified for a combination of two or more elements in one alloy composition, the arithmetic mean of such a combination is compared to the sum of the mean values of the same individual elements, or any combination thereof, in another alloy composition. (b) Addition or deletion of not more than one alloying element with limits having an arithmetic mean of not more than 0.30 percent or addition or deletion of not more than one combination of elements expressed as an alloying element with limits having a combined arithmetic mean of not more than 0.40 percent. (c) Substitution of one alloying element for another element serving the same purpose. (d) Change in limits for impurities expressed singly or as a combination. (e) Change in limits for grain refining elements. (f ) Maximum iron or silicon limits of 0.12 percent and 0.10 percent, or less, respectively, reflecting use of high purity base metal. An alloy shall not be registered as a modification if it meets the requirements for a national variation.
3.3 Experimental Alloys Experimental alloys are also designated in accordance with this system, but they are indicated by the prefix X. The prefix is dropped when the alloy is no longer experimental. During development and before they are designated as experimental, new alloys are identified by serial numbers assigned by their originators. Use of the serial number is discontinued when the X number is assigned.
January 2010
National variations of wrought aluminum and wrought aluminum alloys registered by another country in accor dance with this system are identified by a serial letter following the numerical designation. The serial letters are assigned internationally in alphabetical sequence starting with A but omitting I, O and Q. A national variation has composition limits that are similar but not identical to those registered by another country, with differences such as: (a) Change of not more than the following amounts in arithmetic mean of the limits for an individual alloying element or combination of elements expressed as an alloying element, or both: Arithmetic Mean of Limits for Alloying Elements in Original Alloy or modification
Maximum Change
Up thru 1.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 1.0 thru 2.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 2.0 thru 3.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 3.0 thru 4.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 4.0 thru 5.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 5.0 thru 6.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 6.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.15 0.20 0.25 0.30 0.35 0.40 0.50
To determine compliance when maximum and mini mum limits are specified for a combination of two or more elements in one alloy composition, the arithmetic mean of such a combination is compared to the sum of the mean values of the same individual elements, or any combination thereof, in another alloy composition. (b) Substitution of one alloying element for another element serving the same purpose. (c) Different limits on impurities except for low iron. Iron maximum of 0.12 percent, or less, reflecting high purity base metal, should be considered as an alloy modification. (d) Different limits on grain refining elements. (e) Inclusion of a minimum limit for iron or silicon, or both. Wrought aluminum and wrought aluminum alloys meeting these requirements shall not be registered as a new alloy or alloy modification.
IV-9
4. Cast Aluminum and Aluminum Alloy Designation System Q A system of four digit numerical designations is used to identify aluminum and aluminum alloys in the form of castings and foundry ingot. The first digit indicates the alloy group as follows: Aluminum, 99.00 percent minimum and greater . . . . . . . . . . Aluminum alloys grouped by major alloying elements W E R Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon, with added copper and/or magnesium . . . . . . . . . Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnesium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Zinc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other element . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Unused series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1xx.x 2xx.x 3xx.x 4xx.x 5xx.x 7xx.x 8xx.x 9xx.x 6xx.x
The alloy group in the 2xx.x through 9xx.x excluding 6xx.x alloys is determined by the alloying element present in the greatest mean percentage, except in cases in which the alloy being registered qualified as a modification of a previously registered alloy. If the greatest mean percentage is common to more than one alloying element, the alloy group will be determined by the sequence shown above. The second two digits identify the aluminum alloy or indicate the aluminum purity. The last digit, which is separated from the others by a decimal point, indicates the product form: that is, castings or ingot. A modification of the original alloy or impurity limits is indicated by a serial letter before the numerical designation. The serial letters are assigned in alphabetical sequence starting with A but omitting I, O, Q and X, the X being reserved for experimental alloys. A modification of the original alloy is limited to any one or a combination of the following: (a) Change of not more than the following amounts in the arithmetic mean of the limits for an individual alloying element or combination of elements expressed as an alloying element or both: Arithmetic Mean of Limits for Alloying Elements in Original Alloy
Maximum Change
Up thru 1.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 1.0 thru 2.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 2.0 thru 3.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 3.0 thru 4.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 4.0 thru 5.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 5.0 thru 6.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . Over 6.0 percent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
0.15 0.20 0.25 0.30 0.35 0.40 0.50
To determine compliance when maximum and mini mum limits are specified for a combination of two or more elements in one alloy composition, the arithmetic mean of such a combination is compared to the sum of the mean values of the same individual elements, or any combination thereof, in another alloy composition. (b) Addition or deletion of not more than one alloying element with limits having an arithmetic mean of not more For all numbered footnotes, see page IV-9.
IV-10
than 0.30 percent or addition or deletion of not more than one combination of elements expressed as an alloying element with limits having a combined arithmetic mean of not more than 0.40 percent. (c) Substitution of one alloying element for another ele ment serving the same purpose. (d) Change in limits for impurities expressed singly or as a combination. (e) Change in limits for grain refining elements. (f ) Iron or silicon maximum limits of 0.12 percent and 0.10 percent, or less, respectively, reflecting use of high purity base metal.
4.1 Aluminum Castings and Ingot In the 1xx.x group for minimum aluminum purities of 99.00 percent and greater, the second two of the four digits in the designation indicate the minimum aluminum percentage.T These digits are the same as the two digits to the right of the decimal point in the minimum aluminum percentage when it is expressed to the nearest 0.01 percent. The last digit, which is to the right of the decimal point, indicates the product form: 1xx.0 indicates castings, and 1xx.1 indicates ingot.
4.2 Aluminum Alloy Castings and Ingot In the 2xx.x through 9xx.x alloy groups the second two of the four digits in the designation have no special signifi cance but serve only to identify the different aluminum alloys in the group. The last digit, which is to the right of the decimal point, indicates the product form: xxx.0 indicates castings, xxx.1 indicates ingot that has chemical composition limits conforming to 3.2.1, and xxx.2 indi cates ingot that has chemical composition limits that differ but fall within the limits of xxx.1 ingot.
4.2.1 Limits for Alloying Elements and Impurities Limits for alloying elements and impurities for xxx.1 ingot are the same as for the alloy in the form of castings, except for the following: Maximum Iron Percentage: For All Forms of Castings Up thru 0.15 . . . . . . . . . . . . . . . . . . . . . Over 0.15 thru 0.25 . . . . . . . . . . . . . . . Over 0.25 thru 0.6 . . . . . . . . . . . . . . . . Over 0.6 thru 1.0 . . . . . . . . . . . . . . . . . Over 1.0 . . . . . . . . . . . . . . . . . . . . . . .
For Ingot, Fe shall be Least 0.03 less than castings 0.05 less than castings 0.10 less than castings 0.2 less than castings 0.3 less than castings
Minimum Magnesium Percentage*: For All Forms of Castings For Ingot Less than 0.50 . . . . . . . . . . . . . . . . . . . 0.05 more than castings 0.50 and greater . . . . . . . . . . . . . . . . . 0.1 more than castings Maximum Zinc Percentage: For Die Castings For Ingot Over 0.25 thru 0.6 . . . . . . . . . . . . . . . . 0.10 less than castings Over 0.6 . . . . . . . . . . . . . . . . . . . . . . . 0.1 less than castings *Applicable only if the resulting magnesium range is 0.15 percent or greater.
January 2010
4.2.2 Identifiers for 3xx.x and 4xx.x Foundry Ingot containing Structure Modifiers One of the applicable suffixes in the table below should be added to the registered alloy designation whenever a structure modifier is intentionally added to that alloy. Chemical Composition Limits
Alloy Designation Suffix
Structure Modifying Element
Minimum (%)
Maximum (%)
N S C P
Na Sr Ca P
0.003 0.005 0.005 —
0.08 0.08 0.15 0.060
(a) The letter suffix follows and is separated from the registered foundry ingot designation by a hyphen (e.g., “A356.1-S”)
January 2010
(b) In cases where more than one modifier is intentionally added, only the modifier of greater concentration shall be identified by suffix letter affixed to the registered alloy designation. (c) Where a foundry alloy is sold with a suffix added to its alloy designation, the modifying element’s concentration is not to be included in “Others, Each” or “Others, Total”. (d) It is not intended that these structure modifier identifiers be treated as new alloy registration, not should these designations be listed in the Registration Record.
4.3 Experimental Alloys Experimental alloys are also designated in accordance with this system, but they are indicated by the prefix X. The prefix is dropped when the alloy is no longer experimental. During development and before they are designated as experimental, new alloys are identified by serial numbers assigned by their originators. Use of the serial number is discontinued when the X number is assigned.
IV-11
5. Effect of Alloying Elements 1xxx series—Aluminum of 99 percent or higher purity has many applications, especially in the electrical and chemical fields. These compositions are characterized by excellent corrosion resistance, high thermal and electrical conductivity, low mechanical properties and excellent workability. Moderate increases in strength may be obtained by strainhardening. Iron and silicon are the major impurities. 2xxx series—Copper is the principal alloying element in this group. These alloys require solution heat-treatment to obtain optimum properties; in the heat treated condition mechanical properties are similar to, and sometimes exceed, those of mild steel. In some instances artificial aging is employed to further increase the mechanical properties. This treatment materially increases yield strength, with attendant loss in elongation; its effect on tensile (ultimate) strength is not so great. The alloys in the 2xxx series do not have as good corrosion resistance as most other aluminum alloys, and under certain conditions they may be subject to intergranular corrosion. Therefore, these alloys in the form of sheet are usually clad with a high-purity alloy or a magnesium-silicon alloy of the 6xxx series, which provides galvanic protection to the core material and thus greatly increases resistance to corrosion. Alloy 2024 is perhaps the best known and most widely used aircraft alloy. 3xxx series—Manganese is the major alloying element of alloys in this group, which are generally non-heat-treatable. Because only a limited percentage of manganese, up to about 1.5 percent, can be effectively added to aluminum, it is used as a major element in only a few instances. One of these, however, is the popular 3003, which is widely used as a general purpose alloy for moderate-strength applications requiring good workability. 4xxx series—The major alloying element of this group is silicon, which can be added in sufficient quantities to cause substantial lowering of the melting point without producing brittleness in the resulting alloys. For these reasons aluminum-silicon alloys are used in welding wire and as brazing alloys where a lower melting point than that of the parent metal is required. Most alloys in this series are
IV-12
non-heat-treatable, but when used in welding heat-treatable alloys they will pick up some of the alloying constituents of the latter and so respond to heat treatment to a limited extent. The alloys containing appreciable amounts of silicon become dark grey when anodic oxide finishes are applied, and hence are in demand for architectural applications. 5xxx series—Magnesium is one of the most effective and widely used alloying elements for aluminum. When it is used as the major alloying element or with manganese, the result is a moderate to high strength non-heat-treatable alloy. Magnesium is considerably more effective than manganese as a hardener, about 0.8 percent magnesium being equal to 1.25 percent manganese, and it can be added in considerably higher quantities. Alloys in this series possess good welding characteristics and good resistance to corrosion in marine atmosphere. However, certain limitations should be placed on the amount of cold work and on the safe operating temperatures permissible for the higher magnesium content alloys (over about 3½ percent for operating temperatures above about 150°F) to avoid susceptibility to stress corrosion. 6xxx series—Alloys in this group contain silicon and magnesium in approximate proportions to form magnesium silicide, thus making them heat-treatable. The major alloy in this series is 6061, one of the most versatile of the heattreatable alloys. Though less strong than most of the 2xxx or 7xxx alloys, the magnesium-silicon (or magnesium-silicide) alloys possess good formability and corrosion resistance, with medium strength. Alloys in this heat-treatable group may be formed in the T4 temper (solution heat-treated but not artificially aged) and then reach full T6 properties by artificial aging. 7xxx series—Zinc is the major alloying element in this group, and when coupled with a smaller percentage of magnesium results in heat-treatable alloys of very high strength. Usually other elements such as copper and chromium are also added in small quantities. The outstanding member of this group is 7075, which is among the highest strength alloys available and is used in air-frame structures and for highly stressed parts.
January 2010
6. Temper Designation System Y The temper designation system is used for all forms of wrought and cast aluminum and aluminum alloys except ingot. It is based on the sequences of basic treatments used to produce the various tempers. The temper designation follows the alloy designation, the two being separated by a hyphen. Basic temper designations consist of letters. Sub divisions of the basic tempers, where required, are indicated by one or more digits following the letter. These designate specific sequences of basic treatments, but only operations recognized as significantly influencing the characteristics of the product are indicated. Should some other variation of the same sequence of basic operations be applied to the same alloy, resulting in different characteristics, then additional digits are added to the designation.
6.1 Basic Temper Designations F as fabricated. Applies to the products of shaping processes in which no special control over thermal conditions or strain hard ening is employed. For wrought products, there are no mechanical property limits. O annealed. Applies to wrought products that are annealed to obtain the lowest strength temper, and to cast products that are annealed to improve ductility and dimensional stability. The O may be followed by a digit other than zero. H strain-hardened (wrought products only). Applies to products that have their strength increased by strain-hardening, with or without supplementary thermal treatments to produce some reduction in strength. The H is always followed by two or more digits. W solution heat-treated. An unstable temper applicable only to alloys that spontaneously age at room temperature after solution heat-treatment. This designation is specific only when the period of natural aging is indicated; for example: W ½ hr. T thermally treated to produce stable tempers other than F, O, or H. Applies to products that are thermally treated, with or without supplementary strain-hardening, to produce stable tempers. The T is always followed by one or more digits.
6.2 Subdivisions of Basic Tempers
ment. The number following this designation indicates the degree of strain-hardening. H2 strain-hardened and partially annealed. Applies to products that are strain-hardened more than the desired final amount and then reduced in strength to the desired level by partial annealing. For alloys that age-soften at room temperature, the H2 tempers have the same minimum ultimate tensile strength as the corresponding H3 tempers. For other alloys, the H2 tempers have the same minimum ultimate tensile strength as the corresponding H1 tempers and slightly higher elongation. The number following this designation indicates the degree of strain-hardening remaining after the product has been partially annealed. H3 strain-hardened and stabilized. Applies to products that are strain-hardened and whose mechanical properties are stabilized either by a low temperature thermal treatment or as a result of heat introduced during fabrication. Stabilization usually improves ductility. This designation is applicable only to those alloys that, unless stabilized, gradually age-soften at room temperature. The number following this designation indicates the degree of strain-hardening remaining after the stabilization treatment. H4 strain-hardened and lacquered or painted. Applies to products which are strain-hardened and which are subjected to some thermal operation during the subsequent painting or lacquering operation. The number following this designation indicates the degree of strain-hardening remaining after the product has been thermally treated, as part of painting/ lacquering cure operation. The corresponding H2X or H3X mechanical property limits apply.
6.2.1.2 The digit following the designation H1, H2, H3, and H4 indicates the degree of strain-hardening as identi fied by the minimum value of the ultimate tensile strength. Numeral 8 has been assigned to the hardest tempers normally produced. The minimum tensile strength of tempers HX8 may be determined from Table 1 and is based on the minimum tensile strength of the alloy in the annealed temper. However, temper registrations prior to 1992 that do not conform to the requirements of Table 1 shall not be revised and registrations of intermediate or modified tempers for such alloy/temper systems shall conform to the registration requirements that existed prior to 1992.
6.2.1 Subdivision of H Temper: Strain-hardened
Table 1
6.2.1.1 The first digit following the H indicates the specific combination of basic operations, as follows: H1 strain-hardened only. Applies to products that are strain-hardened to obtain the desired strength without supplementary thermal treat-
US Customary Units Minimum tensile strength in annealed temper ksi
Y Temper designations conforming to this standard for wrought aluminum and wrought aluminum alloys, and aluminum alloy castings may be registered with the Aluminum Association provided: (1) the temper is used or is available for use by more than one user, (2) mechanical property limits are registered, (3) the characteristics of the temper are significantly different from those of all other tempers that have the same sequence of basic treatments and for which designations already have been assigned for the same alloy and product, and (4) the following are also registered if characteristics other than mechanical properties are considered significant: (a) test methods and limits for the characteristics or (b) the specific practices used to produce the temper.
January 2010
up to 6 7 to 9 10 to 12 13 to 15 16 to 18 19 to 24 25 to 30 31 to 36 37 to 42
43 and over
Increase in tensile strength to HX8 temper ksi 8 9 10 11 12 13 14 15 16 17
IV-13
6.2.2 Subdivision of T Temper: Thermally Treated
Metric Units Minimum tensile strength in annealed temper MPa
up to 40 45 to 60 65 to 80 85 to 100 105 to 120 125 to 160 165 to 200 205 to 240 245 to 280
285 and 320 325 and over
Increase in tensile strength to HX8 temper MPa 55 65 75 85 90 95 100 105 110 115 120
Tempers between O (annealed) and HX8 are designated by numerals 1 through 7. (a) Numeral 4 designates tempers whose ultimate tensile strength is approximately midway between that of the O temper and that of the HX8 tempers; (b) Numeral 2 designates tempers whose ultimate tensile strength is approximately midway between that of the O temper and that of the HX4 tempers; (c) Numeral 6 designates tempers whose ultimate tensile strength is approximately midway between that of the HX4 tempers and that of the HX8 tempers; (d) Numerals 1, 3, 5 and 7 designate, similarly, tem pers intermediate between those defined above. (e) Numeral 9 designates tempers whose minimum ultimate tensile strength exceeds that of the HX8 tempers by 2 ksi or more. (For Metric Units by 10 MPa or more). The ultimate tensile strength of the odd numbered intermediate (-HX1, -HX3, -HX5, and HX7) tempers, determined as described above, shall be rounded to the nearest multiple of 0.5 ksi. (For Metric Units when not ending in 0 or 5 shall be rounded to the next higher 0 or 5 MPa). 6.2.1.3 The third digit,U when used, indicates a variation of a two-digit temper. It is used when the degree of control of temper or the mechanical properties or both differ from, but are close to, that (or those) for the two-digit H temper designation to which it is added, or when some other characteristic is significantly affected. (See Appendix for assigned three-digit H tempers.) NOTE: The minimum ultimate tensile strength of a three-digit H temper must be at least as close to that of the corresponding two-digit H temper as it is to the adjacent two-digit H tempers. Products in the H temper whose mechanical properties are below H__1 shall be variations of H__1. U Numerals 1 through 9 may be arbitrarily assigned as the third digit and registered with the Aluminum Association for an alloy and product to indicate a variation of a two-digit H temper (see note Y).
IV-14
6.2.2.1 Numerals 1 through 10 following the T indicate specific sequences of basic treatments, as follows:I T1 cooled from an elevated temperature shaping process and naturally aged to a substantially stable condition. Applies to products that are not cold worked after cooling from an elevated temperature shaping process, or in which the effect of cold work in flattening or straightening may not be recognized in mechanical property limits. T2 cooled from an elevated temperature shaping process, cold worked, and naturally aged to a substantially stable condition. Applies to products that are cold worked to improve strength after cooling from an elevated temperature shaping process, or in which the effect of cold work in flattening or straightening is recognized in mechanical property limits. T3 solution heat-treated,O cold worked, and naturally aged to a substantially stable condition. Applies to products that are cold worked to improve strength after solution heat-treatment, or in which the effect of cold work in flattening or straightening is recognized in mechanical property limits. T4 solution heat-treated O and naturally aged to a substan tially stable condition. Applies to products that are not cold worked after solution heat-treatment, or in which the effect of cold work in flattening or straightening may not be recognized in mechanical property limits. T5 cooled from an elevated temperature shaping process and then artificially aged. Applies to products that are not cold worked after cooling from an elevated temperature shaping process, or in which the effect of cold work in flattening or straight ening may not be recognized in mechanical property limits. T6 solution heat-treated O and then artificially aged. Applies to products that are not cold worked after solution heat-treatment, or in which the effect of cold work in flattening or straightening may not be recognized in mechanical property limits. T7 solution heat-treatedO and overaged/stabilized. Applies to wrought products that are artificially aged after solution heattreatment to carry them beyond a point of maximum strength to provide control of some significant characteristicP. Applies to cast products that are artificially aged after solution heat-treatment to provide dimensional and strength stability. T8 solution heat-treated,O cold worked, and then artificially aged. Applies to products that are cold worked to improve strength, or in which the effect of cold work in flattening or straightening is recognized in mechanical property limits. T9 solution heat-treated,O artificially aged, and then cold worked. Applies to products that are cold worked to improve strength. T10 cooled from an elevated temperature shaping process, cold worked, and then artificially aged. Applies to products that are cold worked to improve strength, or in which the effect of cold work in flattening or straightening is recognized in mechanical property limits. I A period of natural aging at room temperature may occur between or after the operations listed for the T tempers. Control of this period is exercised when it is metallurgically important. O Solution heat treatment is achieved by heating cast or wrought products to a suitable temperature, holding at that temperature long enough to allow constituents to enter into solid solution and cooling rapidly enough to hold the constituents in solution. Some 6xxx series alloys attain the same specified mechanical properties whether furnace solution heat treated or cooled from an elevated temperature shaping process at a rate rapid enough to hold con stituents in solution. In such cases the temper designations T3, T4, T6, T7, T8, and T9 are used to apply to either process and are appropriate designations. P For this purpose, characteristic is something other than mechanical properties. The test method and limit used to evaluate material for this characteristic are specified at the time of the temper registration.
January 2010
6.2.2.2 Additional digits,{ the first of which shall not be zero, may be added to designations T1 through T10 to indicate a variation in treatment that significantly alters the product characteristics that are or would be obtained using the basic treatment. (See Appendix for specific additional digits for T tempers.)
H321
A2 Additional Digits for T Tempers
APPENDIX 6.3 Variations of O Temper: Annealed A digit following the O, when used, indicates a product in the annealed condition having special characteristics. NOTE: As the O temper is not part of the strain-hardened (H) series, variations of O temper shall not apply to products that are strain-hardened after annealing and in which the effect of strain-hardening is recognized in the mechanical properties or other characteristics. A1 Three-Digit H Tempers
A2.1 Assigned Additional Digits for Stress-Relieved Temper The following specific additional digits have been assigned for stress-relieved tempers of wrought products: A2.1.1 Stress relieved by stretching} T_51 Applies to plate and rolled or cold-finished rod or bar, die or ring forgings and rolled rings when stretched the indicated amounts after solution heat treatment or after cooling from an elevated temperature shaping process. The products receive no further straightening after stretching. Plate . . . . . . . . . . . . . . . . . . . . . . . . . 1½% to 3% permanent set.
(a) The following three-digit H temper designations have been assigned for wrought products in all alloys: H_11 Applies to products that incur sufficient strain hardening after the final anneal that they fail to qualify as annealed but not so much or so consistent an amount of strain hardening that they qualify as H_1. H112 Applies to products that may acquire some temper from working at an elevated temperature and for which there are mechanical property limits.
(b) The following three-digit H temper designations have been assigned for pattern or embossed sheet H114 H124, H224, H324 H134, H234, H334 H144, H244, H344 H154, H254, H354 H164, H264, H364 H174, H274, H374 H184, H284, H384 H194, H294, H394 H195, H295, H395
Applies to products from alloys in the 5xxx series, for which the magnesium content is 3% nominal or more. Products are normally thermally stabilized at the last operation to specified stable tensile property limits and meet specified levels of corrosion resistance in accelerated type corrosion tests. They are suitable for continuous service at temperatures no greater than 150°F (66°C). Corrosion tests include inter-granular and exfoliation.
Rolled or Cold-Finished Rod and Bar . . . . . . . . . . . . . . . . . . . . . 1% to 3% permanent set. Die or Ring Forgings and Rolled Rings . . . . . . . . . . . . . . . . . . . . 1% to 5% permanent set. T_510 Applies to extruded rod, bar, profiles (shapes) and tube and to drawn tube when stretched the indicated amounts after solution heat treatment or after cooling from an elevated temperature shaping process. These products receive no further straightening after stretching. Extruded Rod Bar, Profiles (Shapes) and Tube . . . . . . . . . . . . . . . . . . . . . . . . 1% to 3% permanent set. Drawn Tube . . . . . . . . . . . . . . . . . . . . ½% to 3% permanent set.
fabricated from O temper H11, H21, H31 temper, respectively H12, H22, H32 temper, respectively H13, H23, H33 temper, respectively H14, H24, H34 temper, respectively H15, H25, H35 temper, respectively H16, H26, H36 temper, respectively H17, H27, H37 temper, respectively H18, H28, H38 temper, respectively H19, H29, H39 temper, respectively
(c) The following three-digit H temper designations have been assigned only for wrought products in the 5xxx series, for which the magnesium content is 3% nominal or more:
T_511 Applies to extruded rod, bar, profiles (shapes) and tube and to drawn tube when stretched the indicated amounts after solution heat treatment or after cooling from an elevated temperature shaping process. These products may receive minor straightening after stretching to comply with standard tolerances. Extruded Rod, Bar, Profiles (Shapes) and Tube . . . . . . . . . . . . . . . . . . . . . . . . 1% to 3% permanent set. Drawn Tube . . . . . . . . . . . . . . . . . . . . ½% to 3% permanent set.
A2.1.2 Stress relieved by compressing2 T_52 Applies to products that are stress-relieved by compressing after solution heat treatment or cooling from an elevated temperature shaping process to produce a permanent set of 1 percent to 5 percent.
H116 Applies to products manufactured from alloys in the 5xxx series, for which the magnesium content is 3% nominal or more. Products are normally strain hardened at the last operation to specified stable tensile property limits and meet specified levels of corrosion resistance in accelerated type corrosion tests. They are suitable for continuous service at temperature no greater than 150°F (66°C). Corrosion tests include inter-granular and exfoliation.
A2.1.3 S tress relieved by combined stretching and compressing2
{ Additional digits may be arbitrarily assigned and registered with The Aluminum Association for an alloy and product to indicate a variation of tempers T1 through T10 even though the temper representing the basic treatment has not been registered (see note ^). Variations in treatment that do not alter the characteristics of the product are considered alternate treatments for which additional digits are not assigned.
The following temper designations have been assigned for wrought products which are artificially overaged to obtain a
January 2010
T_54 Applies to die forgings that are stress relieved by restriking cold in the finish die.
A2.2 Assigned Additional Digits for T7 Temper Variations
2
The same digits (51, 510, 511, 52, 54) may be added to the designation W to indicate unstable solution heat-treated and stress-relieved tempers.
IV-15
good comprise among exfoliation corrosion resistance, stress corrosion resistance, fracture toughness, and tensile strength. The designations shall be applied when standardizing new alloy-temper-product combinations. T79 Very limited overaging to achieve some improved corrosion resistance with limited reduction in strength as compared to the T6 temper. T76 Limited overaged condition to achieve moderate corrosion resistance with some reduction in strength. The T76 temper has lower strength and better corrosion resistance than the T79 temper. T74 Overaged condition to achieve good corrosion resistance with a greater reduction in strength than the T76 temper. The T74 temper strength and corrosion resistance properties are between those of the T73 and T76 tempers.
treatment for capability demonstration of temper conver sion. When the purchaser requires capability demonstrations from T-temper, the seller shall note “Capability Demonstration” adjacent to the specified and ending tempers. Some examples are: (a) “-T3 to -T82 Capability Demonstration for response to aging”; (b) “-T4 to -T62 Capability Demonstration for response to aging”; (c) “-T4 to -T762 Capability Demonstration for response to overaging”;
T73 Fully overaged condition to achieve the best corrosion resistance of the T7X tempers with a greater reduction in strength than the T74 temper.
(d) “-T6 to -T732 Capability Demonstration for response to overaging”;
T77 Aged condition which provides strength at or near T6 temper and corrosion resistance similar to T76 temper corrosion resistance similar to T76 temper.
(e) “-T351 to -T42 Capability Demonstration for response to re-solution heat-treatment”.
The evolution of material properties from temper T79 to T73 is illustrated in Figure 1.*
A2.3.3 Temper Designation for Purchaser/ User Heat-treatment
Property
Temper
T6
T79
T76
T74
T73
+ Strength
Temper designation T_2 should also be applied to wrought products heat-treated by the purchaser/user, in accordance with the applicable heat treatment specification, to achieve the properties applicable to the final temper.
-
+
A3 Assigned O Temper Variations
Corrosion Resistance
-
Figure 1 * The T77 temper does not fall within the continuous progression of the T7X tempers depicted in Figure 1.
A2.3 Assigned Temper Designations for Producer/ Supplier and Purchaser/User Heat Treatment A2.3.1 Temper Designations for Producer/ Supplier Laboratory Demonstration of Response to Heat-treatment: The following temper designations have been assigned for wrought products test material, furnace heat-treated from annealed (O, O1, etc.) or F temper, to demonstrate response to heat-treatment. T42 Solution heat-treated from annealed or F temper and naturally aged to a substantially stable condition. T62 Solution heat-treated from annealed or F temper and artificially aged. T7_2 Solution heat-treated from annealed or F temper and artificially overaged to meet the mechanical properties and corrosion resistance limits of the T7_ temper.
A2.3.2 Temper Designations for Producer/ Supplier Demonstration of Response to Temper Conversion: Temper designation T_2 shall be used to indicate wrought product test material, which has undergone furnace heatIV-16
The following temper designation has been assigned for wrought products high temperature annealed to accentuate ultrasonic response and provide dimensional stability. O1 Thermally treated at approximately same time and temperature required for solution heat treatment and slow cooled to room temperature. Applicable to products that are to be machined prior to solution heat treatment by the user. Mechanical property limits are not applicable.
A4 Designation of Unregistered Tempers A4.1 The letter P has been assigned to denote H, T and O temper variations that are negotiated between manufac turer and purchaser. The letter P immediately follows the temper designation that most nearly pertains. Specific examples where such designation may be applied include the following: (a) The use of the temper is sufficiently limited so as to preclude its registration. (Negotiated H temper variations were formerly indicated by the third digit zero.) (b) The test conditions (sampling location, number of samples, test specimen configuration, etc.) are different from those required for registration with The Aluminum Association. (c) The mechanical property limits are not established on the same basis as required for registration with The Aluminum Association. (d) For products such as Aluminum Metal Matrix Composites which are not included in any registration records. January 2010
Table 1 COMPARATIVE CHARACTERISTICS AND APPLICATIONS Machinability T
Brazeability Y
Gas
Arc
Resistance Spot and Seam
A A A B B A A A B C A A A B B C B D .. C D C ..
E E D D D E E D D D E E D D D A A A D B B B B
A A A A A A A A A A A A A A A D D D D D D D D
A A A A A A A A A A A A A A A D D D D D D D D
A A A A A A A A A A A A A A A D D D D B B B C
B A A A A B A A A A B A A A A D D D B B B B B
.. DE DE D D .. D C C D D D .. DE DE D D D A A A A A A A A A A A
.. C C B B .. C .. A B C C .. C C B B C A A A A A A A A A A A
.. C D C D .. .. B B D .. .. .. C D D D .. A A B C C B A B B C C
D B B B B B B C C B .. B .. B B B B B E E D D D D D D C C C
D D D D D D D D D D D D D D D D D D A A A A A A B B B B B
D C D D D D D C D D D D D A A A A D A A A A A A A A A A A
D B C C C C B B B C C C A A A A A C A A A A A A A A A A A
D B B B B B B B B B B B B A A A A B B A A A A A B A A A A
1060-O H12 H14 H16 H18 1100-O H12 H14 H16 H18 1350-O H12, H111 H14, H24 H16, H26 H18 2011-T3 T4, T451 T8 2014-O T3, T4, T451 T6, T651, T6510, T6511 2017-T4, T451 2018-T61
A A A A A A A A A A A A A A A DE DE D .. DE D DE
2024-O T4, T3, T351, T3510, T3511 T361 T6 T861, T81, T851, T8510, T8511 T72 2025-T6 2036-T4 2117-T4 2124-T851 2218-T61 T72 2219-O T31, T351, T3510, T3511 T37 T81, T851, T8510, T8511 T87 2618-T61 3003-O H12 H14 H16 H18 H25 3004-O H32 H34 H36 H38
StressCorrosion Cracking 2
..
A A A A A A A A A A A A A A A D D B .. C C C ..
General Q
ALLOY AND TEMPER
WELDABILITY Y
Workability (Cold) T
RESISTANCE TO CORROSION
SOME APPLICATIONS OF ALLOYS
Chemical equipment, railroad tank cars
Sheet metal work, spun hollowware, fin stock
Electrical conductors
Screw machine products
Truck frames, aircraft structures
Screw machine products, fittings Aircraft engine cylinders, heads and pistons Truck wheels, screw machine products, aircraft structures
Forgings, aircraft propellers Auto body panel sheet Rivets Aircraft structures Jet engine impellers and rings Structural uses at high temperatures (to 600°F) High strength weldments
Aircraft engines Cooking utensils, chemical equipment, pressure vessels, sheet metal work, builder’s hardware, storage tanks
Sheet metal work, storage tanks
For all numbered footnotes, see page IV-20.
January 2010
IV-17
Table 1 COMPARATIVE CHARACTERISTICS AND APPLICATIONS (Continued) Machinability T
Brazeability Y
Gas
Arc
Resistance Spot and Seam
5154-O H32 H34 H36 H38 5252-H24 H25 H28
Workability (Cold) T
3105-O H12 H14 H16 H18 H25 4032-T6 5005-O H12 H14 H16 H18 H32 H34 H36 H38 5050-O H32 H34 H36 H38 5052-O H32 H34 H36 H38 5056-O H111 H12, H32 H14, H34 H18, H38 H192 H392 5083-O H321 I H111 H116 I 5086-O H32 I H34 H36 H38 H111 H116 I
StressCorrosion Cracking 2
ALLOY AND TEMPER
WELDABILITY Y
General Q
RESISTANCE TO CORROSION
A A A A A A C A A A A A A A A A A A A A A A A A A A AR AR AR AR AR BR BR AR AR AR AR AR AR AR AR AR AR AR AR AR AR AR AR
A A A A A A B A A A A A A A A A A A A A A A A A A A BR BR BR BR CR DR DR AR AR BR AR AR AR BR BR BR AR AR AR AR AR AR AR
A A A
A A A
A B B C C B .. A A B C C A B C C A A B C C A B B C C A A B B C D D B C C C A B B C C B B A B B C C B B C
E E D D D D B E E D D D E D D D E D D C C D D C C C D D D C C B B D D D D D D C C C D D D D C C C D C C
A A A A A A D B B B B B B B B B B B B B B C C C C C D D D D D D D D D D D D D D D D D D D D D D D C C C
A A A A A A D A A A A A A A A A A A A A A A A A A A C C C C C C C C C C C C C C C C C C C C C C C A A A
A A A A A A B A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A A
B A A A A A C B A A A A A A A A B A A A A B A A A A B A A A A A A B A A A B A A A A A A B A A A A A A A
SOME APPLICATIONS OF ALLOYS
Residential siding, mobile homes, rain carrying goods, sheet metal work
Pistons Appliances, utensils, architectural, electrical conductor
Builder’s hardware, refrigerator trim, coiled tubes
Sheet metal work, hydraulic tube, appliances
Cable sheathing, rivets for magnesium, screen wire, zipper
Unfired, welded pressure vessels, marine, auto aircraft cryogenics, TV towers, drilling rigs, transportation equipment, missile components
Welded structures, storage tanks, pressure vessels, salt water service
Automotive and appliance trim
For all numbered footnotes, see page IV-20.
IV-18
January 2010
Table 1 COMPARATIVE CHARACTERISTICS AND APPLICATIONS (Continued) Machinability T
Brazeability Y
Gas
Arc
Resistance Spot and Seam
AR AR AR AR AR A A A A BR BR BR A A A A A A A A A A .. .. A A B A
A B B C C A B B B B C C A A B B C C A B B C .. .. .. A B C
D D C C C D D C D D D D E D D C C C D D D D .. E C D C C
D D D D D D D D D D D D B C C C C C B B B B A B B A A A
C C C C C C C C C C C C A A A A A A A A A A A A A A A A
A A A A A A A A A A A A A A A A A A A A A A A A A A A A
B A A A A B A A A B A A B B A A A A A A A A A B A B A A
A A A A A C C C B B A A ..
A A A A A A B B B B A A ..
B B B C C B C C B C C B ..
D D C C C D C B C C C D ..
A A A A A D D D D D A A B
A A A A A D D D A A A A ..
A A A A A B B B A A A A ..
A A A A A B B B A A A A ..
6201-T81
A
A
..
C
A
A
A
A
6262-T6, T651, T6510, T6511 T9 6351-T1 T4 T5 T6
B B .. A A A
A A .. .. .. ..
C D C C C C
B B C C C C
B B C C C C
B B B B B B
B B A A A A
A A B B A A
ALLOY AND TEMPER
General Q
Workability (Cold) T
WELDABILITY Y
StressCorrosion Cracking 2
RESISTANCE TO CORROSION
5254-O H32 H34 H36 H38 5454-O H32 H34 H111 5456-O H321 I H116 I 5457-O 5652-O H32 H34 H36 H38 5657-H241 H25 H26 H28 6005-T1, T5 6053-O T6, T61 6061-O T4, T451, T4510, T4511 T6, T651, T652, T6510, T6511
AR AR AR AR AR A A A A AR AR AR A A A A A A A A A A .. .. A B B B
6063-T1 T4 T5, T452 T6 T83, T831, T832 6066-O T4, T4510, T4511 T6, T6510, T6511 6070-T4, T4511 T6 6101-T6, T63 T61, T64 6151-T6, T652
SOME APPLICATIONS OF ALLOYS
Hydrogen peroxide and chemical storage vessels
Welded structures, pressure vessels, marine service
High strength welded structures, pressure vessels, marine applications, storage tanks Hydrogen peroxide and chemical storage vessels
Anodized auto and appliance trim
Wire and rod for rivets Heavy-duty structures requiring good corrosion resistance, truck and marine, railroad cars, furniture, pipelines Pipe railing, furniture, architectural extrusions
Forgings and extrusion for welded structures Heavy duty welded structures, pipelines High strength bus conductors Moderate strength, intricate forgings for machine and auto parts High strength electric conductor wire Screw machine products Extruded shapes, structurals, pipe and tube
For all numbered footnotes, see page IV-20.
January 2010
IV-19
Table 1 COMPARATIVE CHARACTERISTICS AND APPLICATIONS (Continued) Brazeability Y
Gas
Arc
Resistance Spot and Seam
A A A .. .. C C
A A A .. .. B B
B B C .. .. D D
D C C .. .. B B
A A A A B D D
A A A A C D D
A A A A A D D
A A A A A B B
Extruded architectural and trim sections
.. CE C C .. CE .. C C A A A
.. C B B .. C .. C B A A A
.. D D D .. D .. D D A A A
D B B B .. B .. B B D E D
D D D D D D D D D A A A
D D D D D D D D D A A A
D D D C D D D B D A A A
B B B B B B B B B A A A
Aircraft and other structures
StressCorrosion Cracking 2
Machinability T
6463-T1 T5 T6 6951-T42, T62 7005-T53 7049-T73, T7352 7050-T73510, T73511 T74 U, T7451 U, T74510 U, T74511 U, T7452 U, T7651, T76510, T76511 7075-O T6, T651, T652, T6510, T6511 T73, T7351 7175-T74, T7452, T7454 7178-O T6, T651, T6510, T6511 7475-O 7475-T61, -T651 7475-T761, T7351 8017-H12, H22, H221 8030-H12, H221 8176-H14, H24
General Q
ALLOY AND TEMPER
WELDABILITY Y
Workability (Cold) T
RESISTANCE TO CORROSION
SOME APPLICATIONS OF ALLOYS
Aircraft forgings Aircraft and other structures
Aircraft and other structures Shell Casings Aircraft & Other Structures Electrical conductors Electrical conductors Electrical conductors
Q Ratings A through E are relative ratings in decreasing order of merit, based on exposures to sodium chloride solution by intermittent spraying or immersion. Alloys with A and B ratings can be used in industrial and seacoast atmospheres without protection. Alloys with C, D and E ratings generally should be protected at least on faying surfaces. W Stress-corrosion cracking ratings are based on service experience and on laboratory tests of specimens exposed to the 3.5% sodium chloride alternate immersion test. A = No known instance of failure in service or in laboratory tests. B = No known instance of failure in service; limited failures in laboratory tests of short transverse specimens. C = Service failures with sustained tension stress acting in short transverse direction relative to grain structure; limited failures in laboratory tests of long transverse specimens. D = Limited service failures with sustained longitudinal or long transverse areas. These ratings are neither product specific nor test direction specific and therefore indicate only the general level of stress-corrosion cracking resistance. For more specific information on certain alloys, see ASTM G64. E In relatively thick sections the rating would be E. R This rating may be different for material held at elevated temperature for long periods. T Ratings A through D for Workability (cold), and A through E for Machinability, are relative ratings in decreasing order of merit. Y Ratings A through D for Weldability and Brazeability are relative ratings defined as follows: A = Generally weldable by all commercial procedures and methods. B = Weldable with special techniques or for specific applications that justify preliminary trials or testing to develop welding procedure and weld performance. C = Limited weldability because of crack sensitivity or loss in resistance to corrosion and mechanical properties. D = No commonly used welding methods have been developed. U T74 type tempers, although not previously registered, have appeared in various literature and specifications as T736 type tempers. I 5xxx products in the -H116 and H32X tempers have similar mechanical properties; however, production methods and testing requirements differ, and these tempers are not interchangeable. The -H116 temper is typically used in marine and other applications requiring demonstration of exfoliation resistance.
IV-20
January 2010
Table 2 FOREIGN ALLOY DESIGNATIONS AND SIMILAR AA ALLOYS
Foreign Alloy Designation
Designating Country
Al99 Al99,5 E-Al AlCuMg1 AlCuMg2 AlCuMg0,5 AlMg5 AlMgSi0,5 E-AlMgSi AlZnMgCu1,5
Austria (Önorm) Q
990C CB60 CG30 CG42 CG42 Alclad CM41 CN42 CS41N CS41N Alclad CS41P GM31N GM41 GM50P GM50R GR20 GS10 GS11N GS11P MC10 S5 SG11P SG121 ZG62 ZG62 Alclad A5/L A45 A-G1 A-G0.6 A-G4MC A-GS A-GS/L A-M1 A-M1G A-U4G A-U2G A-U2GN A-U4G1 A-U4N A-U4SG A-S12UN A-Z5GU E-A1995 R 3.0257 T AlCuBiPb R 3.1655 T AlCuMg0.5 R 3.1305 T AlCuMg1 R 3.1325 T AlCuMg2 R 3.1355 T AlCuSiMn R 3.1255 T AlMg4.5Mn R 3.3547 T AlMgSi0.5 R 3.3206 T AlSi5 R 3.2245 T E-AlMgSi0.5 R 3.3207 T AlZnMgCu1.5 R 3.4365 T
January 2010
Canada (CSA) W
France (NF) E
} } } } } } } } } } }
Equivalent or Similar AA Alloy 1200 1050 1350 2017 2024 2117 5056 6063 6101 7075 1100 2011 2117 2024 Alclad 2024 2017 2018 2014 Alclad 2014 2025 5454 5083 5356 5056 5052 6063 6061 6053 3003 4043 6151 4032 7075 Alclad 7075 1350 1100 5050 5005 5086 6063 6101 3003 3004 2017 2117 2618 2024 2218 2014 4032 7075 1350 2011 2117 2017 2024
Germany
2014 5083 6063
Foreign Alloy Designation 1E 91E H14 H19 H20 L.80, L.81 L.86 L.87 L.93, L.94 L.95, L.96 L.97, L.98 2L.55, 2L.56 2L.58 3L.44 5L.37 6L.25 N8 N21 150A 324A 372B 717, 724, 731A 745, 5014, 5084 5090 5100 P-AlCu4MgMn P-AlCu4.5MgMn P-AlCu4.5MgMnplacc. P-AlCu2.5MgSi P-AlCu4.4SiMnMg P-AlCu4.4SiMnMgplacc. P-AlMg0.9 P-AlMg1.5 P-AlMg2.5 P-AlSi0.4Mg P-AlSi0.5Mg Al99.5E L-313 L-314 L-315 L-371 Al-Mg-Si Al1.5Mg Al-Cu-Ni Al3.5Cu0.5Mg Al4Cu1.2Mg Al-Zn-Mg-Cu Al-Zn-Mg-Cu-pl Al99.0Cu AlCu2Mg AlCu4Mg1 AlCu4SiMg AlCu4MgSi AlMg1 AlMg1.5 AlMg2.5 AlMg3.5 AlMg4 AlMg5 AlMn1Cu AlMg3Mn AlMg4.5Mn AlMgSi AlMg1SiCu AIZn6MgCu
Designating Country
Equivalent or Similar AA Alloy 1350 6101 2017 6063 6061 5052 2117 2117 2014A 7075 2024 5052 5056 5050 2017 2218 5083 4043
Great Britain (BS) Y
Great Britain (DTD) U
}
Italy (UNI) I
Spain (UNE) O
Switzerland (VSM) P
ISO {
2017 4032 6063 2618 2024 Alclad 2024 2017 2024 Alclad 2024 2117 2014 Alclad 2014 5657 5050 5052 6063 6101 1350 2014 2024 2218 7075 6101 5050 2218 2017 2027 7075 Alclad 7075 1100 2117 2024 2014 2017 5005 5050 5052 5154 5086 5056 3003 5454 5083 6063 6061 7075
4043 6101 7075
Q Austrian Standard M3430. W Canadian Standards Association. E Normes Françaises. R Deutsche Industrie-Norm. T Werkstoff-Nr. Y British Standard. U Directorate of Technical Development. I Unificazione Nazionale Italiana. O Una Norma Espanol. P Verein Schweizerischer Maschinenindustrieller. { International Organization for Standardization.
IV-21
Table 3 MECHANICAL PROPERTY LIMITS FOR COMMONLY USED ALUMINUM SAND CASTING ALLOYS 1 Alloy
Temper 2
201.0 204.0 208.0 222.0 222.0 242.0 242.0 242.0 242.0 295.0 295.0 295.0 295.0 319.0 319.0 319.0 328.0 328.0 355.0 355.0 355.0 355.0 C355.0 356.0 356.0 356.0 356.0 356.0 A356.0 357.0 A357.0 359.0 443.0 B433.0 512.0 514.0 520.0 535.0 705.0 707.0 707.0 710.0 712.0 713.0 771.0 771.0 771.0 771.0 771.0 771.0 850.0 851.0 852.0
T7 T4 F 0 T61 0 T571 T61 T77 T4 T6 T62 T7 F T5 T6 F T6 T51 T6 T7 T71 T6 F T51 T6 T7 T71 T6 — — — F F F F T4 5 F or T5 F or T5 T5 T7 F or T5 F or T5 F or T5 T5 T51 T52 T53 T6 T71 T5 T5 T5
MINIMUM PROPERTIES Tensile Strength Ultimate Yield (0.2% Offset) ksi ( MPa ) ksi ( MPa ) 60.0 ( 415 ) 50.0 ( 345 ) 45.0 ( 310 ) 28.0 ( 195 ) 19.0 ( 130 ) 12.0 ( 85 ) 23.0 ( 160 ) — — 30.0 ( 205 ) — — 23.0 ( 160 ) — — 29.0 ( 200 ) — — 32.0 ( 220 ) 20.0 ( 140 ) 24.0 ( 165 ) 13.0 ( 90 ) 29.0 ( 200 ) 13.0 ( 90 ) 32.0 ( 220 ) 20.0 ( 140 ) 36.0 ( 250 ) 28.0 ( 195 ) 29.0 ( 200 ) 16.0 ( 110 ) 23.0 ( 160 ) 13.0 ( 90 ) 25.0 ( 170 ) — — 31.0 ( 215 ) 20.0 ( 140 ) 25.0 ( 170 ) 14.0 ( 95 ) 34.0 ( 235 ) 21.0 ( 145 ) 25.0 ( 170 ) 18.0 ( 125 ) 32.0 ( 220 ) 20.0 ( 140 ) 35.0 ( 240 ) — — 30.0 ( 205 ) 22.0 ( 150 ) 35.0 ( 250 ) 25.0 ( 170 ) 19.0 ( 130 ) — — 23.0 ( 160 ) 16.0 ( 110 ) 30.0 ( 205 ) 20.0 ( 140 ) 31.0 ( 215 ) 29.0 ( 200 ) 25.0 ( 170 ) 18.0 ( 125 ) 34.0 ( 235 ) 24.0 ( 165 ) — — — — — — — — — — — — 17.0 ( 115 ) 7.0 ( 50 ) 17.0 ( 115 ) 6.0 ( 40 ) 17.0 ( 115 ) 10.0 ( 70 ) 22.0 ( 150 ) 9.0 ( 60 ) 42.0 ( 290 ) 22.0 ( 150 ) 35.0 ( 240 ) 18.0 ( 125 ) 30.0 ( 205 ) 17.0 ( 115 ) 33.0 ( 230 ) 22.0 ( 150 ) 37.0 ( 255 ) 30.0 ( 205 ) 32.0 ( 220 ) 20.0 ( 140 ) 34.0 ( 235 ) 25.0 ( 170 ) 32.0 ( 220 ) 22.0 ( 150 ) 42.0 ( 290 ) 38.0 ( 260 ) 32.0 ( 220 ) 27.0 ( 165 ) 36.0 ( 250 ) 30.0 ( 205 ) 36.0 ( 250 ) 27.0 ( 185 ) 42.0 ( 290 ) 35.0 ( 240 ) 48.0 ( 330 ) 45.0 ( 310 ) 16.0 ( 110 ) — — 17.0 ( 115 ) — — 24.0 ( 165 ) 18.0 ( 125 )
% Elongation in 2 inches or 4 times diameter 3.0 6.0 1.5 — — — — — 1.0 6.0 3.0 — 3.0 1.5 — 1.5 1.0 1.0 — 2.0 — — 2.5 2.0 — 3.0 — 3.0 3.5 — — — 3.0 3.0 — 6.0 12.0 9.0 5.0 2.0 1.0 2.0 4.0 3.0 1.5 3.0 1.5 1.5 5.0 2.0 5.0 3.0 —
Typical Brinell Hardness 4 500 – kgf load 10 – mm ball 110–140 — 40–70 65–95 100–130 55–85 70–100 90–120 60–90 45–75 60–90 80–110 55–85 55–85 65–95 65–95 45–75 65–95 50–80 70–105 70–100 60–95 75–105 40–70 45–75 55–90 60–90 45–75 70–105 — — — 25–55 25–55 35–65 35–65 60–90 60–90 50–80 70–100 65–95 60–90 60–90 60–90 85–115 70–100 70–100 — 75–105 105–135 30–60 30–60 45–75
1 Values represent properties obtained from separately cast lest bars and are derived from ASTM 8-26, Standard Specification for Aluminum-Alloy Sand Castings; Federal Specification QQ-A-601e, Aluminum Alloy Sand Castings; and Military Specification MIL-A-21180c, Aluminum Alloy Castings, High Strength. Unless otherwise specified, the tensile strength, yield strength and elongation values of specimens cut from castings shall be not less than 75 percent of the tensile and yield strength values and not less than 25 percent of the elongation values given above. The customer should keep in mind that (1) some foundries may offer additional tempers for the above alloys, and (2) foundries are constantly improving casting techniques and, as a result, some may offer minimum properties in excess of the above. If quality level 4 castings are specified as described in Table 1 of AA-CS-M5-85, no tensile tests shall be specified nor tensile requirements be met on specimens cut from castings. 2 F indicates “as cast” condition; refer to AA-CS-M11 for recommended times and temperatures of heat treatment for other tempers to achieve properties specified. 3 Footnote no longer in use. 4 Hardness values are given for information only; not required for acceptance. 5 The T4 temper of Alloy 520.0 is unstable; significant room temperature aging occurs within life expectancy of most castings. Elongation may decrease by as much as 80 percent.
IV-22
January 2010
Table 4 MECHANICAL PROPERTY LIMITS FOR COMMONLY USED PERMANENT MOLD CASTING ALLOYS 1 Alloy
Temper 2
204.0 208.0 208.0 208.0 222.0 222.0 242.0 242.0 298.0 308.0 319.0 319.0 332.0 333.0 333.0 333.0 333.0 336.0 336.0 354.0 354.0 355.0 355.0 355.0 355.0 355.0 C355.0 356.0 356.0 356.0 356.0 356.0 A356.0 357.0 A357.0 359.0 359.0 443.0 B443.0 A444.0 513.0 535.0 705.0 707.0 711.0 713.0 850.0 851.0 851.0 852.0
T4 T4 T6 T7 T551 T65 T571 T61 T6 F F T6 T5 F T5 T6 T7 T551 T65 T61 T62 T51 T6 T62 T7 T71 T61 F T51 T6 T7 T71 T61 T6 T61 T61 T62 F F T4 F F T5 T7 T1 T5 T5 T5 T6 T5
ksi 48.0 33.0 35.0 33.0 30.0 40.0 34.0 40.0 35.0 24.0 28.0 34.0 31.0 28.0 30.0 35.0 31.0 31.0 40.0 48.0 52.0 27.0 37.0 42.0 36.0 34.0 40.0 21.0 25.0 33.0 25.0 25.0 37.0 45.0 45.0 45.0 47.0 21.0 21.0 20.0 22.0 35.0 37.0 45.0 28.0 32.0 18.0 17.0 16.0 27.0
MINIMUM PROPERTIES Tensile Strength Ultimate Yield (0.2% Offset) ( MPa ) ksi ( MPa ) ( 330 ) 29.0 ( 200 ) ( 230 ) 15.0 ( 105 ) ( 240 ) 22.0 ( 150 ) ( 230 ) 16.0 ( 110 ) ( 205 ) — — ( 275 ) — — ( 230 ) — — ( 275 ) — — ( 240 ) — — ( 165 ) — — ( 195 ) 14.0 ( 95 ) ( 235 ) — — ( 215 ) — — ( 195 ) — — ( 205 ) — — ( 240 ) — — ( 215 ) — — ( 215 ) — — ( 275 ) — — ( 330 ) 37.0 ( 255 ) ( 360 ) 42.0 ( 290 ) ( 185 ) — — ( 255 ) — — ( 290 ) — — ( 250 ) — — ( 235 ) 27.0 ( 185 ) ( 275 ) 30.0 ( 205 ) ( 145 ) — — ( 170 ) — — ( 230 ) 22.0 ( 150 ) ( 170 ) — — ( 170 ) — — ( 255 ) 26.0 ( 180 ) ( 310 ) — — ( 310 ) 36.0 ( 250 ) ( 310 ) 34.0 ( 235 ) ( 325 ) 38.0 ( 260 ) ( 145 ) 7.0 ( 50 ) ( 145 ) 6.0 ( 40 ) ( 140 ) — — ( 150 ) 12.0 ( 85 ) ( 240 ) 18.0 ( 125 ) ( 255 ) 17.0 ( 120 ) ( 310 ) 35.0 ( 240 ) ( 195 ) 18.0 ( 125 ) ( 220 ) 22.0 ( 150 ) ( 125 ) — — ( 115 ) — — ( 125 ) — — ( 185 ) — —
% Elongation in 2 inches or 4 times diameter 8.0 4.5 2.0 3.0 — — — — 2.0 2.0 1.5 2.0 — — — — — — — 3.0 2.0 — 1.5 — — — 3.0 3.0 — 3.0 3.0 3.0 5.0 3.0 3.0 4.0 3.0 2.0 2.5 20.0 2.5 8.0 10.0 3.0 7.0 4.0 8.0 3.0 8.0 3.0
Typical Brinell Hardness 3 500 – kgf load 10 – mm ball — 60–90 75–105 65–95 100–130 125–155 90–120 95–125 75–105 55–85 70–100 75–105 90–120 65–100 70–106 65–115 75–105 90–120 110–140 — — 60–90 75–105 90–120 70–100 85–95 75–105 40–70 55–85 65–95 60–90 60–90 70–100 75–105 85–115 75–105 85–115 30–60 30–60 — 45–75 60–90 55–85 80–110 55–86 60–90 30–60 30–60 — 55–85
1 Values represent properties obtained from separately cast test bars and are derived from ASTM B-108, Standard Specification for Aluminum-Alloy Permanent Mold Castings; Federal Specification QQ-A-596d, Aluminum Alloy Permanent and Semi-Permanent Mold Castings; and Military Specification MIL-A-21180c, Aluminum Alloy Castings, High Strength. Unless otherwise specified, the average tensile strength, average yield strength and average elongation values of specimens cut from castings shall be not less than 75 percent of the tensile strength and yield values and not less than 25 percent of the elongation values given above. The customer should keep in mind that (1) some foundries may offer additional tempers for the above alloys, and (2) foundries are constantly improving casting techniques and, as a result, some may offer minimum properties in excess of the above. 2 F indicates “as cast” condition; refer to AA-CS-M11 for recommended times and temperatures of heat treatment for other tempers to achieve properties specified. 3 Hardness values are given for information only; not required for acceptance.
January 2010
IV-23
Table 5 MECHANICAL PROPERTY LIMITS OF FASTENER ALLOYS Q TENSILE STRENGTH ksi min. YIELD W
ELONGATION W percent min. in. 2 in. or 4D E
ULTIMATE SHEARING STRENGTH ksi min.
32.0
12
33.0
..
..
37.0
40.0
10
37.0
18
26.0
35.0
6
30.0
20.0
14
20.0
42.0
35.0
10
25.0
70.0
58.0
10
39.0
0.063–1.000
77.0
66.0
7
42.0
0.063–1.000
68.0
56.0
10
41.0
0.063–1.000
84.0
73.0
5
46.0
SPECIFIED DIAMETER in.
ULTIMATE
2017-T4
0.063–1.000
55.0
2024-T42
0.063–0.124
62.0
0.125–1.000
62.0
2117-T4
0.063–1.000
38.0
18.0
2219-T6
0.063–1.000
55.0
6053-T61
0.063–1.000
30.0
6061-T6
0.063–1.000
7050-T7
0.063–1.000
7075-T6 7075-T73 7178-T6
ALLOY AND TEMPER
Q Rivet and cold heading wire and rod, and the fasteners produced from it, shall upon proper heat treatment (T4 and T42 tempers) or heat treatment and aging (T6, T61, T7 and T73 tempers) be capable of developing the properties presented in Table 10.4. Tensile tests are preferred for the rivet and cold heading wire and rod, and shear tests for the fasteners made from it. W The measurement of elongation and yield strength is not required for wire less than 0.125 inch in thickness or diameter. E D represents specimen diameter.
Table 5M MECHANICAL PROPERTY LIMITS OF FASTENER ALLOYS Q TENSILE STRENGTH MPa min ULTIMATE YIELD W
ELONGATION W percent min
ALLOY AND TEMPER
SPECIFIED DIAMETER mm
2017-T4
1.60–25.00
380
2024-T42
1.60–3.15
425
..
..
..
255
3.15–25.00
425
255
10
9
255
2117-T4
1.60–25.00
260
125
18
16
180
2219-T6
1.60–25.00
380
240
6
5
205
6053-T61
1.60–25.00
205
135
14
12
135
6061-T6
1.60–25.00
290
240
10
9
170
7050-T7
1.60–25.00
485
400
10
9
270
7075-T6
1.60–25.00
530
455
7
6
290
7075-T73
1.60–25.00
470
385
10
9
280
7178-T6
1.60–25.00
580
500
5
4
315
220
50 mm 12
5D (5.65 A ) 10
ULTIMATE SHEARING STRENGTH MPa min 225
Q Rivet and cold heading wire and rod, and the fasteners produced from it, shall upon proper heat treatment (T4 and T42 tempers) or heat treatment and aging (T6, T61, T7 and T73 tempers) be capable of developing the properties presented in Table 10.4. Tensile tests are preferred for the rivet and cold heading wire and rod, and shear tests for the fasteners made from it. W Processes such as flattening, leveling, or straightening coiled products subsequent to shipment by the producer may alter the mechanical properties of the metal.
IV-24
January 2010
Table 6 TYPICAL MECHANICAL PROPERTIES Q W are intended only as a basis for comparing alloys and tempers and should not be specified as engineering requirements or used for design purposes.
TENSION
4 11 13 15 18 5 15 17 20 22 4 12 14 16 24 43 45 14 42 60 10 40 37 60 10 40 46 11 50 47 57 11 45 42 63 60 66 37 28 24 64 37 11 27 36 46 42 51 57
N
Alclad 2024-O Alclad 2024-T3 Alclad 2024-T4, T351 Alclad 2024-T361 U Alclad 2024-T81, T851 Alclad 2024-T861 U 2025-T6 2036-T4 2117-T4 2124-T851 2218-T72 2219-O 2219-T42 2219-T31, T351 2219-T37 2219-T62 2219-T81, T851 2219-T87
1 ⁄16 in. Thick Specimen
1 ⁄2 in. Diameter Specimen
43 16 12 8 6 35 12 9 6 5 .. .. .. .. .. .. .. .. .. .. 21 20 22 10 .. .. .. 20 18 20 13 20 18 19 11 6 6 .. 24 .. .. .. 18 20 17 11 10 10 10
.. .. .. .. .. 45 25 20 17 15 . . T .. .. .. . . Y
FO
10 12 14 16 19 13 16 18 21 24 12 14 16 18 27 55 59 27 62 70 25 63 61 68 26 62 61 27 70 68 72 26 65 64 67 65 70 58 49 43 70 48 25 52 52 57 60 66 69
O T
1060-O 1060-H12 1060-H14 1060-H16 1060-H18 1100-O 1100-H12 1100-H14 1100-H16 1100-H18 1350-O 1350-H12 1350-H14 1350-H16 1350-H19 2011-T3 2011-T8 2014-O 2014-T4, T451 2014-T6, T651 Alclad 2014-O Alclad 2014-T3 Alclad 2014-T4, T451 Alclad 2014-T6, T651 2017-O 2017-T4, T451 2018-T61 2024-O 2024-T3 2024-T4, T351 2024-T361 U
YIELD
FATIGUE
MODULUS
BRINNELL NUMBER
ULTIMATE SHEARING STRENGTH
ENDURANCE E Limit
MODULUS R OF ELASTICTY
500 kg load 10 mm ball
ksi
ksi
ksi × 103
19 23 26 30 35 23 28 32 38 44 .. .. .. .. .. 95 100 45 105 135 .. .. .. .. 45 105 120 47 120 120 130 .. .. .. .. .. .. 110 .. 70 .. 95 .. .. .. .. .. .. ..
7 8 9 10 11 9 10 11 12 13 8 9 10 11 15 32 35 18 38 42 18 37 37 41 18 38 39 18 41 41 42 18 40 40 41 40 42 35 .. 28 .. 30 .. .. .. .. .. .. ..
3 4 5 6.5 6.5 5 6 7 9 9 .. .. .. .. 7 18 18 13 20 18 .. .. .. .. 13 18 17 13 20 20 18 .. .. .. .. .. .. 18 18 O
10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.2 10.2 10.6 10.6 10.6 10.5 10.5 10.5 10.5 10.5 10.5 10.8 10.6 10.6 10.6 10.6 10.6 10.6 10.6 10.6 10.6 10.6 10.4 10.3 10.3 10.6 10.8 10.6 10.6 10.6 10.6 10.6 10.6 10.6
ES
ULTIMATE
ELONGATION percent in 2 in.
SHEAR
D
STRENGTH ksi
15 12 18 20 13 .. .. .. .. 22 22 12 22 .. 19 .. .. .. .. .. .. .. 19 .. 27 8 11 .. .. .. .. .. .. ..
R
ALLOY AND TEMPER
HARDNESS
IG N
The following typical properties are not guaranteed, since in most cases they are averages for various sizes, product forms and methods of manufacture and may not be exactly representative of any particular product or size. These data
14 .. .. .. .. .. .. 15 15 15
For all numbered footnotes, see page IV-28.
January 2010
IV-25
Table 6 TYPICAL MECHANICAL PROPERTIES (Continued) Q W
54 6 18 21 25 27 6 18 21 25 27 10 25 29 33 36 10 25 29 33 36 8 19 22 25 28 20 22 23 24 26 46 6 19 22 25 28 17 20 24 27 8 21 24 26 29 13 28 31 35 37 22 59 50
N
1 ⁄16 in. Thick Specimen
1 ⁄2 in. Diameter Specimen
.. 30 10 8 5 4 30 10 8 5 4 20 10 9 5 5 20 10 9 5 5 24 7 5 4 3 11 10 8 9 8 .. 25 10 6 5 4 11 8 6 5 24 9 8 7 6 25 12 10 8 7 .. .. ..
10 40 20 16 14 10 40 20 16 14 10 25 17 12 9 6 25 17 12 9 6 .. .. .. .. .. ..
FO
64 16 19 22 26 29 16 19 22 26 29 26 31 35 38 41 26 31 35 38 41 17 22 25 28 31 24 26 26 24 26 55 18 20 23 26 29 20 23 26 29 21 25 28 30 32 28 33 38 40 42 42 63 60
O T
2618-T61 3003-O 3003-H12 3003-H14 3003-H16 3003-H18 Alclad 3003-O Alclad 3003-H12 Alclad 3003-H14 Alclad 3003-H16 Alclad 3003-H18 3004-O 3004-H32 3004-H34 3004-H36 3004-H38 Alclad 3004-O Alclad 3004-H32 Alclad 3004-H34 Alclad 3004-H36 Alclad 3004-H38 3105-O 3105-H12 3105-H14 3105-H16 3105-H18 3105-H22 3105-H24 3105-H25 3105-H26 3105-H28 4032-T6 5005-O 5005-H12 5005-H14 5005-H16 5005-H18 5005-H32 5005-H34 5005-H36 5005-H38 5050-O 5050-H32 5050-H34 5050-H36 5050-H38 5052-O 5052-H32 5052-H34 5052-H36 5052-H38 5056-O 5056-H18 5056-H38
YIELD
FATIGUE
MODULUS
BRINNELL NUMBER
ULTIMATE SHEARING STRENGTH
ENDURANCE E Limit
MODULUS R OF ELASTICTY
ksi
ksi
ksi × 103
38 11 12 14 15 16 11 12 14 15 16 16 17 18 20 21 16 17 18 20 21 12 14 15 16 17 14 15 15 16 17 38 11 14 14 15 16 14 14 15 16 15 17 18 19 20 18 20 21 23 24 26 34 32
18 7 8 9 10 10 .. .. .. .. .. 14 15 15 16 16 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 16 .. .. .. .. .. .. .. .. .. 12 13 13 14 14 16 17 18 19 20 20 22 22
10.8 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 11.4 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.2 10.2 10.2 10.2 10.2 10.3 10.3 10.3
500 kg load 10 mm ball 115 28 35 40 47 55 .. .. .. .. .. 45 52 63 70 77 .. .. .. .. .. .. .. .. .. .. ..
ES IG
ULTIMATE
ELONGATION percent in 2 in.
SHEAR
D
STRENGTH ksi
R
ALLOY AND TEMPER
HARDNESS
.. .. .. 9 .. .. .. .. .. .. .. .. .. .. .. .. .. .. 30 18 14 10 8 35 10 15
N
TENSION
.. .. .. 120 28 .. .. .. .. 36 41 46 51 36 46 53 58 63 47 60 68 73 77 65 105 100
For all numbered footnotes, see page IV-28.
IV-26
January 2010
Table 6 TYPICAL MECHANICAL PROPERTIES (Continued) Q W TENSION
N
BRINNELL NUMBER
ULTIMATE SHEARING STRENGTH
ENDURANCE E Limit
MODULUS R OF ELASTICTY
1 ⁄2 in. Diameter Specimen
500 kg load 10 mm ball
ksi
ksi
ksi × 103
.. .. .. 22 12 12 10 14 27 15 13 12 10 25 11 5 27 15 13 12 10 25 22 10 10 14 18 .. .. .. .. 22 12 6 25 12 10 8 7 12 7 25 22 12 25 22 12 .. 20 22 12 12 9 10 12
22 16 16 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 24 22 16 16 .. .. .. 30 18 14 10 8 .. .. 30 25 17 .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. 58 67 73 78 80 63 68 75 58 67 73 78 80 63 62 73 81 70 62 .. .. 90 90 32 48 55 47 60 68 73 77 40 50 30 65 95 .. .. .. 25 42 .. 60 73 82 70 95
25 .. .. 23 .. .. 27 .. 22 22 24 26 28 .. 21 23 22 22 24 26 28 .. 23 24 26 23 23 .. .. 30 30 12 16 18 18 20 21 23 24 12 15 12 24 30 11 22 27 10 14 .. 17 22 22 18 27
.. 23 23 .. .. .. .. .. 17 18 19 20 21 17 .. .. 17 18 19 20 21 17 .. .. .. .. .. .. .. .. .. .. .. .. 16 17 18 19 20 .. .. 9 14 14 .. .. .. 8 9 .. 10 10 .. .. ..
10.3 10.3 10.3 10.3 10.3 10.3 10.3 10.3 10.2 10.2 10.2 10.2 10.2 10.2 10.0 10.0 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.2 10.3 10.3 10.3 10.3 10.0 10.0 10.0 10.2 10.2 10.2 10.2 10.2 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0
IG N
21 33 33 17 30 30 37 19 17 30 33 36 39 17 25 35 17 30 33 36 39 17 17 30 35 26 18 23 24 37 37 7 23 27 13 28 31 35 37 20 24 8 21 40 7 19 37 7 13 13 21 31 35 27 39
O T
5457-O 5457-H25 5457-H38, H28 5652-O 5652-H32 5652-H34 5652-H36 5652-H38 5657-H25 5657-H38, H28 6061-O 6061-T4, T451 6061-T6, T651 Alclad 6061-O Alclad 6061-T4, T451 Alclad 6061-T6, T651 6063-O 6063-T1 6063-T4 6063-T5 6063-T6 6063-T83 6063-T831 6063-T832
42 46 46 38 42 42 47 39 35 39 42 45 48 35 34 41 35 39 42 45 48 35 36 40 44 38 36 45 45 51 51 19 26 30 28 33 38 40 42 23 28 18 35 45 17 33 42 13 22 25 27 35 37 30 42
MODULUS
1 ⁄16 in. Thick Specimen
FO
5083-O 5083-H116 { 5083-H321 5086-O 5086-H32 5086-H116 { 5086-H34 5086-H112 5154-O 5154-H32 5154-H34 5154-H36 5154-H38 5154-H112 5252-H25 5252-H38, H28 5254-O 5254-H32 5254-H34 5254-H36 5254-H38 5254-H112 5454-O 5454-H32 5454-H34 5454-H111 5454-H112 5456-O 5456-H112 5456-H116 { 5456-H321 {
YIELD
FATIGUE
ES
ULTIMATE
ELONGATION percent in 2 in.
SHEAR
D
STRENGTH ksi
R
ALLOY AND TEMPER
HARDNESS
For all numbered footnotes, see page IV-28
January 2010
IV-27
Table 6 TYPICAL MECHANICAL PROPERTIES (Continued) Q W TENSION
N
MODULUS
BRINNELL NUMBER
ULTIMATE SHEARING STRENGTH
ENDURANCE E Limit
MODULUS R OF ELASTICTY
1 ⁄16 in. Thick Specimen
1 ⁄2 in. Diameter Specimen
500 kg load 10 mm ball
ksi
ksi
ksi × 103
43 90 120 .. .. 71 120 .. 95 42 60 74 135 135
14 29 34 34 .. 20 35 .. 29 14 17 22 44 43
.. .. 16 14 .. .. 13 .. 13 10 10 10 .. ..
10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.0 10.4 10.4
.. .. .. 60 150 .. .. 135 .. .. .. .. .. .. .. .. .. .. .. .. ..
.. 44 47 22 48 22 46 42 .. .. .. .. .. .. .. .. .. .. .. .. 10
.. .. .. .. 23 .. .. 23 .. .. .. .. .. .. .. .. .. .. .. .. ..
10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.4 10.3 10.4 10.4 10.2 10.4 10.4 10.2 10.4 10.2 10.2 10.0
12 30 52 51 11 28 55 22 41 13 21 31 65 63
.. .. .. 10 .. 15 I .. 20 14 20 12 12 .. ..
18 18 12 .. .. .. 10 .. .. .. .. .. 12 11
72 76 80 33 83 32 76 76 33 88 83 32 81 82 85 72 75 77 75 71 17
63 68 71 15 73 14 67 66 15 78 73 14 71 71 74 61 65 67 66 61 14
.. .. .. 17 11 17 11 .. 15 10 .. 16 10 11 .. .. 12 .. 11 12 15
12 11 11 16 11 .. .. 11 16 11 11 .. .. .. 13 13 .. 12 .. .. ..
D
22 52 57 55 14 32 58 36 45 22 27 35 75 75
FO
O T
6066-O 6066-T4, T451 6066-T6. T651 6070-T6 6101-H111 6101-T6 6262-T9 6351-T4 6351-T6 6463-T1 6463-T5 6463-T6 7049-T73 7049-T7352 7050-T73510, T73511 7050-T7451 P 7050-T7651 7075-O 7075-T6, T651 Alclad 7075-O Alclad 7075-T6, T651 7175-T74 7178-O 7178-T6, T651 7178-T76, T7651 Alclad 7178-O Alclad 7178-T6, T651 7475-T61 7475-T651 7475-T7351 7475-T761 7475-T7651 Alclad 7475-T61 Alclad 7475-T761 8176-H24
YIELD
FATIGUE
N
ULTIMATE
ELONGATION percent in 2 in.
SHEAR
ES IG
STRENGTH ksi
R
ALLOY AND TEMPER
HARDNESS
Q The mechanical property limits are listed by major product in the “Standards Section” of this manual. W The indicated typical mechanical properties for all except 0 temper material are higher than the specified minimum properties. For 0 temper products typical ultimate and yield values are slightly lower than specified (maximum) values. E Based on 500,000,000 cycles of completely reversed stress using the R.R. Moore type of machine and specimen. R Average of tension and compression moduli. Compression modulus is about 2% greater than tension modulus. T 1350-O wire will have an elongation of approximately 23% in 10 inches. Y 1350-H19 wire will have an elongation of approximately 1½% in 10 inches. U Tempers T361 and T861 were formerly designated T36 and T86, respectively. I Based on ¼ in. thick specimen. O Based on 107 cycles using flexural type testing of sheet specimens. P T7451, although not previously registered, has appeared in literature and in some specifications as T73651. { 5xxx products in the -H116 and -H32X tempers have similar mechanical properties; however, production methods and testing requirements differ, and these tempers are not interchangeable. The -H116 temper is typically used in marine and other applications requiring demonstrations of exfoliation resistance.
IV-28
January 2010
Table 6M TYPICAL MECHANICAL PROPERTIES Q W The following typical properties are not guaranteed, since in most cases they are averages for various sizes, product forms and methods of manufacture and may not be exactly representative of any particular product or size. These data TENSION
N
Alclad 2024-O Alclad 2024-T3 Alclad 2024-T4, T351 Alclad 2024-T361 U Alclad 2024-T81, T851 Alclad 2024-T861 U 2025-T6 2036-T4 2117-T4 2124-T851 2218-T72 2219-O 2219-T42 2219-T31, T351 2219-T37 2219-T62 2219-T81, T851 2219-T87
43 16 12 8 6 35 12 9 6 5 .. .. .. .. .. .. .. .. .. .. 21 20 22 10 .. .. .. 20 18 20 13 20 18 19 11 6 6 .. 24 .. .. .. 18 20 17 11 10 10 10
FATIGUE
MODULUS
ULTIMATE SHEARING STRENGTH
ENDURANCE E LIMIT
MODULUS R OF ELASTICITY
MPa
MPa
MPa × 103
50 55 60 70 75 60 70 75 85 90 55 60 70 75 105 220 240 125 260 290 125 255 255 285 125 260 270 125 285 285 290 125 275 275 285 275 290 240 205 195 .. 205 .. .. .. .. .. .. ..
20 30 35 45 45 35 40 50 60 60 .. .. .. .. 50 125 125 90 140 125 .. .. .. .. 90 125 115 90 140 140 125 .. .. .. .. .. .. 125 125 O 95 .. .. .. .. .. .. 105 105 105
69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 70 70 73 73 73 73 73 73 73 73 73 74 73 73 73 73 73 73 73 73 73 73 72 71 71 73 74 73 73 73 73 73 73 73
12.5 mm Diameter 500 kgf load Specimen 10 mm ball .. .. .. .. .. 42 22 18 15 13 . .T .. .. .. . .Y
19 23 26 30 35 23 28 32 38 44 .. .. .. .. .. 95 100 45 105 135 .. .. .. .. 45 105 120 47 120 120 130 .. .. .. .. .. .. 110 .. 70 .. 95 .. .. .. .. .. .. ..
13 10 16 18 11 .. .. .. .. 20 20 10 20 .. 17 .. .. .. .. .. .. .. 17 .. 24 8 9 .. .. .. .. .. .. ..
IG N
30 75 90 105 125 35 105 115 140 150 30 85 95 110 165 295 310 95 290 415 70 275 255 415 70 275 315 75 345 325 395 75 310 290 365 415 455 255 195 165 440 255 75 185 250 315 290 350 395
1.60 mm Thick Specimen
FO
70 85 100 115 130 90 110 125 145 165 85 95 110 125 185 380 405 185 425 485 170 435 421 470 180 425 420 185 485 472 495 180 450 440 460 450 485 400 340 295 485 330 170 360 360 395 415 455 475
O T
1060-O 1060-H12 1060-H14 1060-H16 1060-H18 1100-O 1100-H12 1100-H14 1100-H16 1100-H18 1350-O 1350-H12 1350-H14 1350-H16 1350-H19 2011-T3 2011-T8 2014-O 2014-T4, T451 2014-T6, T651 Alclad 2014-O Alclad 2014-T3 Alclad 2014-T4, T451 Alclad 2014-T6, T651 2017-O 2017-T4, T451 2018-T61 2024-O 2024-T3 2024-T4, T351 2024-T361 U
YIELD
SHEAR
BRINNELL NUMBER
ES
ULTIMATE
ELONGATION percent
HARDNESS
D
STRENGTH MPa
R
ALLOY AND TEMPER
are intended only as a basis for comparing alloys and tempers and should not be specified as engineering requirements or used for design purposes.
For all numbered footnotes, see page IV-32.
January 2010
IV-29
Table 6M TYPICAL MECHANICAL PROPERTIES (Continued) Q W TENSION
N
ELONGATION percent
SHEAR
FATIGUE
MODULUS
BRINNELL NUMBER
ULTIMATE SHEARING STRENGTH
ENDURANCE E LIMIT
MODULUS R OF ELASTICITY
YIELD
1.60 mm Thick Specimen
12.5mm Diameter Specimen
500 kg load 10 mm ball
MPa
MPa
MPa × 103
440 110 130 150 175 200 110 130 150 175 200 180 215 240 260 285 180 215 240 260 285 115 150 170 195 215 165 180 185 195 205 380 125 140 160 180 200 140 160 180 200 145 170 190 205 220 195 230 260 275 290 290 435 415
370 40 125 145 170 185 40 125 145 170 185 70 170 200 230 250 70 170 200 230 250 55 130 150 170 195 140 150 160 165 180 315 40 130 150 170 195 115 140 165 185 55 145 165 180 200 90 195 215 240 255 150 405 345
.. 30 10 8 5 4 30 10 8 5 4 20 10 9 5 5 20 10 9 5 5 24 7 5 4 3 11 10 9 9 8 .. 25 10 6 5 4 11 8 6 5 24 9 8 7 6 25 12 10 8 7 .. .. ..
10 37 18 14 12 9 37 18 14 12 9 22 15 10 8 5 22 15 10 8 5 .. .. .. .. .. .. .. .. .. .. 9 .. .. .. .. .. .. .. .. .. .. .. .. .. .. 27 16 12 9 7 32 9 13
115 28 35 40 47 55 .. .. .. .. .. 45 52 63 70 77 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 120 28 .. .. .. .. 36 41 46 51 36 46 53 58 63 47 60 68 73 77 65 105 100
260 75 85 95 105 110 75 85 95 105 110 110 115 125 140 145 110 115 125 140 145 85 95 105 110 115 95 105 105 110 115 260 75 95 95 105 110 95 95 105 110 105 115 125 130 140 125 140 145 160 165 180 235 220
90 50 55 60 70 70 .. .. .. .. .. 95 105 105 110 110 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 110 .. .. .. .. .. .. .. .. .. 85 90 90 95 95 110 115 125 130 140 140 150 150
73 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 79 69 69 69 69 69 69 69 69 69 69 69 69 69 69 70 70 70 70 70 71 71 71
ES IG
D
R
N
ULTIMATE
O T
2618-T61 3003-O 3003-H12 3003-H14 3003-H16 3003-H18 Alclad 3003-O Alclad 3003-H12 Alclad 3003-H14 Alclad 3003-H16 Alclad 3003-H18 3004-O 3004-H32 3004-H34 3004-H36 3004-H38 Alclad 3004-O Alclad 3004-H32 Alclad 3004-H34 Alclad 3004-H36 Alclad 3004-H38 3105-O 3105-H12 3105-H14 3105-H16 3105-H18 3105-H22 3105-H24 3105-H25 3105-H26 3105-H28 4032-T6 5005-O 5005-H12 5005-H14 5005-H16 5005-H18 5005-H32 5005-H34 5005-H36 5005-H38 5050-O 5050-H32 5050-H34 5050-H36 5050-H38 5052-O 5052-H32 5052-H34 5052-H36 5052-H38 5056-O 5056-H18 5056-H38
STRENGTH MPa
FO
ALLOY AND TEMPER
HARDNESS
For all numbered footnotes, see page IV-32.
IV-30
January 2010
Table 6M TYPICAL MECHANICAL PROPERTIES (Continued) Q W TENSION
N
BRINNELL NUMBER
ULTIMATE SHEARING STRENGTH
ENDURANCE E LIMIT
MODULUS R OF ELASTICITY
12.5 mm Diameter Specimen
500 kg load 10 mm ball
MPa
MPa
MPa × 103
.. .. .. 22 12 12 10 14 27 15 13 12 10 25 11 5 27 15 13 12 10 25 22 10 10 14 18 .. .. .. 22 12 6 25 12 10 8 7 12 7 25 22 12 25 22 12 .. 20 22 12 12 9 10 12
20 14 14 .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. 22 20 14 .. .. .. 27 16 12 9 7 .. .. 27 22 15 .. .. .. .. .. .. .. .. .. .. ..
.. .. .. .. .. .. .. .. 58 67 73 78 80 63 68 75 58 67 73 78 80 63 62 73 81 70 62 .. .. 90 32 48 55 47 60 68 73 77 40 50 30 65 95 .. .. .. 25 42 .. 60 73 82 70 95
170 .. .. 165 .. .. 185 .. 150 150 165 180 195 .. 145 160 150 150 165 180 195 .. 160 165 180 160 160 .. .. 205 85 110 125 125 140 145 160 165 95 105 85 165 205 75 150 185 70 95 .. 115 150 150 125 185
.. 160 160 .. .. .. .. .. 115 125 130 140 145 115 .. .. 115 125 130 140 145 115 .. .. .. .. .. .. .. .. .. .. .. 110 115 125 130 140 .. .. 60 95 95 .. .. .. 55 60 .. 70 70 .. .. ..
71 71 71 71 71 71 71 71 70 70 70 70 70 70 69 69 70 70 70 70 70 70 70 70 70 70 70 71 71 71 69 69 69 70 70 70 70 70 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69 69
IG N
145 230 230 115 205 205 255 130 115 205 230 250 270 115 170 240 115 205 230 250 270 115 115 205 240 180 125 160 165 255 50 160 185 90 195 215 240 255 140 165 55 145 275 50 130 255 50 90 90 145 215 240 185 270
MODULUS
1.60 mm Thick Specimen
FO
290 315 315 260 290 290 325 270 240 270 290 310 330 240 235 285 240 270 290 310 330 240 250 275 305 260 250 310 310 350 130 180 205 195 230 260 275 290 160 195 125 240 310 115 230 290 90 150 170 185 240 255 205 290
O T
5083-O 5083-H116 { 5083-H321 5086-O 5086-H32 5086-H116 { 5086-H34 5086-H112 5154-O 5154-H32 5154-H34 5154-H36 5154-H38 5154-H112 5252-H25 5252-H38, H28 5254-O 5254-H32 5254-H34 5254-H36 5254-H38 5254-H112 5454-O 5454-H32 5454-H34 5454-H111 5454-H112 5456-O 5456-H112 5456-H321, H116 5457-O 5457-H25 5457-H38, H28 5652-O 5652-H32 5652-H34 5652-H36 5652-H38 5657-H25 5657-H38, H28 6061-O 6061-T4, T451 6061-T6, T651 Alclad 6061-O Alclad 6061-T4, T451 Alclad 6061-T6, T651 6063-O 6063-T1 6063-T4 6063-T5 6063-T6 6063-T83 6063-T831 6063-T832
YIELD
FATIGUE
ES
ULTIMATE
ELONGATION percent.
SHEAR
D
STRENGTH MPa
R
ALLOY AND TEMPER
HARDNESS
For all numbered footnotes, see page IV-32.
January 2010
IV-31
Table 6M TYPICAL MECHANICAL PROPERTIES (Continued) Q W TENSION ELONGATION percent
SHEAR
FATIGUE
MODULUS
BRINNELL NUMBER
ULTIMATE SHEARING STRENGTH
ENDURANCE E LIMIT
MODULUS R OF ELASTICITY
YIELD
1.60 mm Thick Specimen
12.5 mm Diameter Specimen
500 kg load 10 mm ball
MPa
MPa
MPa × 103
150 360 395 380 95 220 400 250 310 150 185 240 515 515
85 205 360 350 75 195 380 150 285 90 145 215 450 435
.. .. .. 10 .. 15 I .. 20 14 20 12 12 .. ..
16 16 10 .. .. .. 9 .. .. .. .. .. 10 9
43 90 120 .. .. 71 120 .. 95 42 60 74 135 135
95 200 235 235 .. 140 240 .. 200 95 115 150 305 295
.. .. 110 95 .. .. 90 .. 90 70 70 70 .. ..
69 69 69 69 69 69 69 69 69 69 69 69 72 72
495 525 550
435 470 490
.. .. ..
11 10 10
.. .. ..
.. 305 325
.. .. ..
72 72 72
230 570 220 525 525 230 605 570 220 560 565 585 495 515 530 515 490 160
105 505 95 460 455 105 540 505 95 460 490 510 420 450 460 455 420 95
17 11 17 11 .. 15 10 .. 16 10 11 .. .. 12 .. 11 12 15
60 150 .. .. 135 .. .. .. .. .. .. .. .. .. .. .. .. ..
150 330 150 315 290 .. .. .. .. .. .. .. .. .. .. .. .. 70
.. 160 .. .. 160 .. .. .. .. .. .. .. .. .. .. .. .. ..
72 72 72 72 72 72 72 71 72 72 70 72 72 70 72 70 70 69
ES IG
D
R
14 9 .. .. 10 14 9 9 .. .. .. 13 13 .. 12 .. .. ..
N
ULTIMATE
N
O T
6066-O 6066-T4, T451 6066-T6. T651 6070-T6 6101-H111 6101-T6 6262-T9 6351-T4 6351-T6 6463-T1 6463-T5 6463-T6 7049-T73 7049-T7352 7050-T73510, T73511 7050-T7451 P 7050-T7651 7075-O 7075-T6, T651 Alclad 7075-O Alclad 7075-T6, T651 7175-T74 7178-O 7178-T6, T651 7178-T76, T7651 Alclad 7178-O Alclad 7178-T6, T651 7475-T61 7475-T651 7475-T7351 7475-T761 7475-T7651 Alclad 7475-T61 Alclad 7475-T761 8176-H24
STRENGTH MPa
FO
ALLOY AND TEMPER
HARDNESS
Q The mechanical property limits are listed by major product in the “Standards Section” of this manual. W The indicated typical mechanical properties for all except 0 temper material are higher than the specified minimum properties. For 0 temper products typical ultimate and yield values are slightly lower than specified (maximum) values. E Based on 500,000,000 cycles of completely reversed stress using the R.R. Moore type of machine and specimen. R Average of tension and compression moduli. Compression modulus is about 2% greater than tension modulus. T 1350-O wire will have an elongation of approximately 23% in 10 inches. Y 1350-H19 wire will have an elongation of approximately 1½% in 10 inches. U Tempers T361 and T861 were formerly designated T36 and T86, respectively. I Based on ¼ in. thick specimen. O Based on 107 cycles using flexural type testing of sheet specimens. P T7451, although not previously registered, has appeared in literature and in some specifications as T73651. { 5xxx products in the -H116 and -H32X tempers have similar mechanical properties; however, production methods and testing requirements differ, and these tempers are not interchangeable. The -H116 temper is typically used in marine and other applications requiring demonstrations of exfoliation resistance.
IV-32
January 2010
Table 7 TYPICAL PHYSICAL PROPERTIES—THERMAL AND ELECTRICAL The following typical properties are not guaranteed, since in most cases they are averages for various sizes, product forms and methods of manufacture and may not be exactly representative of any particular product or size. These data
ALLOY
AVERAGE Q COEFFICIENT OF THERMAL EXPANSION
1060
68° TO 212°F per °F 13.1
°F 1195–1215
1100
13.1
1190–1215
1350 2011
13.2 12.7
1195–1215 1005–1190 Y
2014
12.8
945–1180 T
2017
13.1
955–1185 T
2018 2024
12.4 12.9
945–1180 Y 935–1180 T
2025 2036 2117 2124 2218 2219
12.6 13.0 13.2 12.7 12.4 12.4
970–1185 T 1030–1200 Y 1030–1200 Y 935–1180 T 940–1175 T 1010–1190 T
2618 3003
12.4 12.9
1020–1180 1190–1210
3004 3105 4032
13.3 13.1 10.8
1165–1210 1175–1210 990–1060 T
4043 4045 4343 5005 5050 5052 5056
12.3 11.7 12.0 13.2 13.2 13.2 13.4
1065–1170 1065–1110 1070–1135 1170–1210 1155–1205 1125–1200 1055–1180
5083 5086 5154 5252 5254 5356 5454
13.2 13.2 13.3 13.2 13.3 13.4 13.1
1095–1180 1085–1185 1100–1190 1125–1200 1100–1190 1060–1175 1115–1195
5456 5457 5652 5657
13.3 13.2 13.2 13.2
1055–1180 1165–1210 1125–1200 1180–1215
MELTING RANGE W E APPROX.
TEMPER
O H18 O H18 All T3 T8 O T4 T6 O T4 T61 O T3, T4, T361 T6, T81, T861 T6 T4 T4 T851 T72 O T31, T37 T6, T81, T87 T6 O H12 H14 H18 All All O T6 O All All All All All O H38 O All All All All O O H38 O All All All
are intended only as a basis for comparing alloys and tempers and should not be specified as engineering requirements or used for design purposes.
THERMAL CONDUCTIVITY AT 77°F English Units R 1625 1600 1540 1510 1625 1050 1190 1340 930 1070 1340 930 1070 1340 840 1050 1070 1100 1070 1055 1070 1190 780 840 1020 1340 1130 1100 1070 1130 1190 1070 960 1130 1190 1250 1390 1340 960 810 750 810 870 870 960 870 810 930 930 810 1220 960 1420
ELECTRICAL CONDUCTIVITY AT 68°F Percent of International Annealed Copper Standard Equal Volume 62 61 59 57 62 39 45 50 34 40 50 34 40 50 30 38 40 41 40 38 40 44 28 30 37 50 42 41 40 42 45 40 35 42 45 47 52 50 35 29 27 29 31 32 35 32 29 34 34 29 46 35 54
Equal Weight 204 201 194 187 204 123 142 159 108 127 159 108 127 160 96 122 128 135 130 122 126 138 88 94 120 163 137 134 130 137 148 132 116 140 151 158 172 165 116 98 91 98 104 107 116 107 98 113 113 98 153 116 180
ELECTRICAL RESISTIVITY AT 68°F Ohm—Cir. Mil/Foot 17 17 18 18 17 27 23 21 31 26 21 31 26 21 35 27 26 25 26 27 26 24 37 35 28 21 25 25 26 25 23 26 30 25 23 25 20 21 30 36 38 36 33 32 30 32 36 31 31 36 23 30 19
For all numbered footnotes, see page IV-34.
January 2010
IV-33
Table 7 TYPICAL PHYSICAL PROPERTIES—THERMAL AND ELECTRICAL (Continued)
ALLOY
AVERAGE Q COEFFICIENT OF THERMAL EXPANSION 68° TO 212°F per °F
MELTING RANGE W E APPROX.
TEMPER
°F
6005
13.0
1125–1210 Y
6053
12.8
1070–1205 Y
6061
13.1
1080–1205 Y
6063
13.0
1140–1210
6066
12.9
1045–1195 T
6070 6101
.. 13.0
1050–1200 T 1150–1210
6105
13.0
1110–1200 Y
6151
12.9
1090–1200 Y
6201 6262 6351 6463
13.0 13.0 13.0 13.0
1125–1210 Y 1080–1205 Y 1030–1200 1140–1210
6951
13.0
1140–1210
7049 7050 7072 7075 7175 7178 7475
13.0 12.8 13.1 13.1 13.0 13.0 12.9
890–1175 910–1165 1185–1215 890–1175 U 890–1175 U 890–1165 U 890–1175
8017
13.1
1190–1215
8030 8176
13.1 13.1
1190–1215 1190–1215
T1 T5 O T4 T6 O T4 T6 O T1 T5 T6, T83 O T6 T6 T6 T61 T63 T64 T65 T1 T5 O T4 T6 T81 T9 T6 T1 T5 T6 O T6 T73 T74 I O T6 T74 T6 T61, T651 T76, T761 T7351 H12, H22 H212 H221 H24
THERMAL CONDUCTIVITY AT 77°F
ELECTRICAL CONDUCTIVITY AT 68°F Percent of International Annealed Copper Standard
ELECTRICAL RESISTIVITY AT 68°F
English Units R
Equal Volume
Equal Weight
Ohm—Cir. Mil/Foot
1250 1310 1190 1070 1130 1250 1070 1160 1510 1340 1450 1390 1070 1020 1190 1510 1540 1510 1570 1510 1220 1340 1420 1130 1190 1420 1190 1220 1340 1450 1390 1480 1370 1070 1090 1540 900 1080 870 960 1020 1130 .. .. 1600
47 49 45 40 42 47 40 43 58 50 55 53 40 37 44 57 59 58 60 58 46 50 54 42 45 54 44 46 50 55 53 56 52 40 41 59 33 39 31 35 40 42 59 61 61 61
155 161 148 132 139 155 132 142 191 165 181 175 132 122 145 188 194 191 198 191 151 165 178 138 148 180 145 151 165 181 175 186 172 132 135 193 105 124 98 116 132 139 193 200 201 201
22 21 23 26 25 22 26 24 18 21 19 20 26 28 24 18 18 18 17 18 23 21 19 25 23 19 24 23 21 19 20 19 20 26 25 18 31 26 33 30 26 25 18 17 17 17
Q Coefficient to be multiplied by 10−6. Example: 12.2 × 10−6 = 0.0000122. W Melting ranges shown apply to wrought products of ¼ inch thickness or greater. E Based on typical composition of the indicated alloys. R English units = btu-in./ft2hr°F. T Eutectic melting is not eliminated by homogenization. Y Eutectic melting can be completely eliminated by homogenization. U Homogenization may raise eutectic melting temperature 20–40°F but usually does not eliminate eutectic melting. I Although not formerly registered, the literature and some specifications have used T736 as the designation for this temper.
IV-34
January 2010
Table 7M TYPICAL PHYSICAL PROPERTIES—THERMAL AND ELECTRICAL The following typical properties are not guaranteed, since in most cases they are averages for various sizes, product forms and methods of manufacture and may not be exactly representative of any particular product or size. These data
ALLOY
AVERAGE Q COEFFICIENT OF THERMAL EXPANSION
MELTING RANGE W E APPROX.
20° TO 100°C per °C
TEMPER
°C
1060
23.6
645–655
1100
23.6
640–655
1350 2011
23.6 22.9
645–655 540–645 T
2014
23.0
505–635 R
2017
23.6
510–640 R
2018 2024
22.3 23.2
505–640 T 500–635 R
2025 2036 2117 2124 2218 2219
22.7 23.4 23.8 22.9 22.3 22.3
520–640 R 555–650 T 550–650 T 500–635 R 505–635 R 545–645 R
2618 3003
22.3 23.2
550–640 640–655
3004 3105 4032
23.9 23.6 19.4
630–655 635–655 530–570 R
4043 4045 4343 5005 5050 5052 5056
22.0 21.1 21.6 23.8 23.8 23.8 24.1
575–630 575–600 575–615 630–655 625–650 605–650 565–640
5083 5086 5154 5252 5254 5356 5454
23.8 23.8 23.9 23.8 23.9 24.1 23.6
580–640 585–640 590–645 605–650 590–645 575–635 600–645
5456 5457 5652 5657
23.9 23.8 23.8 23.8
570–640 630–655 605–650 635–655
O H18 O H18 All T3 T8 O T4 T6 O T4 T61 O T3, T4, T361 T6, T81, T861 T6 T4 T4 T851 T72 O T31, T37 T6, T81, T87 T6 O H12 H14 H18 All All O T6 O All All All All All O H38 O All All All All O O H38 O All All All
are intended only as a basis for comparing alloys and tempers and should not be specified as engineering requirements or used for design purposes.
THERMAL CONDUCTIVITY AT 25°C
ELECTRICAL CONDUCTIVITY AT 20°C MS/m
ELECTRICAL RESISTIVITY AT 20°C
W/m-K
Equal Volume
Equal Mass
Ohm—mm2/m
234 230 222 218 234 151 172 193 134 155 193 134 155 193 121 151 155 159 155 152 155 172 113 121 146 193 163 159 155 163 172 155 138 163 171 180 201 193 138 117 109 117 126 126 138 126 117 134 134 117 176 138 205
36 35 34 33 36 23 26 29 20 23 29 20 23 29 17 22 23 24 23 22 23 26 16 17 21 29 24 24 23 24 26 23 20 24 26 27 30 29 20 17 16 17 18 19 20 19 17 20 20 17 27 20 31
118 117 113 108 118 71 82 92 63 74 92 63 74 93 56 71 74 78 75 71 73 80 57 58 70 92 78 78 74 79 86 77 67 81 88 92 100 96 67 57 53 57 60 62 67 62 57 66 66 57 89 69 104
0.028 0.029 0.029 0.030 0.028 0.043 0.038 0.034 0.050 0.043 0.034 0.050 0.043 0.034 0.059 0.045 0.043 0.042 0.043 0.045 0.043 0.038 0.062 0.059 0.048 0.034 0.042 0.042 0.043 0.042 0.038 0.043 0.050 0.041 0.038 0.037 0.033 0.034 0.050 0.059 0.062 0.059 0.056 0.053 0.050 0.053 0.059 0.050 0.050 0.059 0.037 0.050 0.032
For all numbered footnotes, see page IV-36.
January 2010
IV-35
Table 7M TYPICAL PHYSICAL PROPERTIES—THERMAL AND ELECTRICAL (Continued)
ALLOY
AVERAGE Q COEFFICIENT OF THERMAL EXPANSION
MELTING RANGE W E APPROX.
20° TO 100°C per °C
°C
6005
23.6
605–655 T
6053
23.0
575–650 T
6061
23.6
580–650 T
6063
23.4
615–655
6066
23.2
560–645 R
6070 6101
.. 23.4
565–650 R 620–655
6105
23.4
600–650 Y
6151
23.2
590–650 T
6201 6262 6351 6463
23.4 23.4 23.4 23.4
610–655 T 580–650 T 555–650 615–655 T
6951
23.4
615–655
7049 7050 7072 7075 7175 7178 7475
23.4 23.0 23.6 23.6 23.4 23.4 23.2
475–635 490–630 640–655 475–635 Y 475–635 Y 475–630 Y 475–635
8017
23.6
645–655
8030 8176
23.6 23.6
645–655 645–655
TEMPER
T1 T5 O T4 T6 O T4 T6 O T1 T5 T6, T83 O T6 T6 T6 T61 T63 T64 T65 T1 T5 O T4 T6 T81 T9 T6 T1 T5 T6 O T6 T73 T74 U O T6 T74 T6 T61, T651 T76, T761 T7351 H12, H22 H212 H221 H24
THERMAL CONDUCTIVITY AT 25°C
ELECTRICAL CONDUCTIVITY AT 20°C MS/m
ELECTRICAL RESISTIVITY AT 20°C
W/m-K
Equal Volume
Equal Mass
Ohm—mm2/m
180 188 172 155 167 180 155 167 218 193 209 201 155 146 172 218 222 218 226 218 176 193 205 163 172 205 172 176 193 209 201 213 197 155 157 222 130 157 126 138 146 163 .. .. 230 230
27 28 26 23 24 27 23 25 34 29 32 31 23 21 26 33 34 34 35 34 27 29 31 24 26 31 26 27 29 32 31 32 30 23 24 34 19 23 18 20 23 24 34 35 35 35
90 93 86 77 81 90 77 82 111 96 105 102 77 71 84 109 113 111 115 111 88 96 103 80 86 104 84 88 96 105 102 108 100 77 78 112 61 72 57 69 77 81 113 117 117 117
0.037 0.036 0.038 0.042 0.041 0.037 0.043 0.040 0.029 0.034 0.031 0.032 0.043 0.048 0.038 0.030 0.029 0.029 0.029 0.029 0.037 0.034 0.032 0.042 0.038 0.032 0.038 0.038 0.034 0.031 0.032 0.031 0.033 0.043 0.042 0.029 0.053 0.043 0.056 0.050 0.043 0.041 0.029 0.029 0.029 0.029
Q Coefficient to be multiplied by 10−6. Example: 23.6 × 10−6 = 0.0000236. W Melting ranges shown apply to wrought products of 6 mm thickness or greater. E Based on typical composition of the indicated alloys. R Eutectic melting is not eliminated by homogenization. T Eutectic melting can be completely eliminated by homogenization. Y Homogenization may raise eutectic melting temperature 10–20°C but usually does not eliminate eutectic melting. U Although not formerly registered, the literature and some specifications have used T736 as the designation for this temper. I MS/m = 0.58 × % IACS.
IV-36
January 2010
Table 8 TYPICAL PHYSICAL PROPERTIES—DENSITY Density and specific gravity are dependent upon composition, and variations are discernible from one cast to another for most alloys. The nominal values shown below should not be specified as engineering requirements but are used in calculating typical values for weight per unit length, weight per Alloy 1050 1060 1100 1145 1175 1200 1230 1235 1345 1350 2011 2014 2017 2018 2024 2025 2036 2117 2124 2218 2219 2618 3003 3004 3005 3105 4032 4043 4045 4047 4145 4343 4643 5005 5050 5052 5056 5083 5086 5154 5183
January 2010
Density (lbs/cu. in.) .0975 .0975 .098 .0975 .0975 .098 .098 .0975 .0975 .0975 .102 .101 .101 .102 .100 .101 .100 .099 .100 .101 .103 .100 .099 .098 .098 .098 .097 .097 .096 .096 .099 .097 .097 .098 .097 .097 .095 .096 .096 .096 .096
Specific Gravity 2.705 2.705 2.71 2.700 2.700 2.70 2.70 2.705 2.705 2.705 2.83 2.80 2.79 2.82 2.78 2.81 2.75 2.75 2.78 2.81 2.84 2.76 2.73 2.72 2.73 2.72 2.68 2.69 2.67 2.66 2.74 2.68 2.69 2.70 2.69 2.68 2.64 2.66 2.66 2.66 2.66
unit area, covering area, etc. The density values are derived from the metric and subsequently rounded. These values are not to be converted to the metric. X.XXX0 and X.XXX5 density values and X.XX0 and X.XX5 specific gravity values are limited to 99.35 percent or higher purity aluminum. Alloy 5252 5254 5356 5454 5456 5457 5554 5556 5652 5654 5657 6003 6005 6053 6061 6063 6066 6070 6101 6105 6151 6162 6201 6262 6351 6463 6951 7005 7008 7049 7050 7072 7075 7175 7178 7475 8017 8030 8176 8177
Density (lbs/cu. in.) .096 .096 .096 .097 .096 .097 .097 .096 .097 .096 .097 .097 .097 .097 .098 .097 .098 .098 .097 .097 .098 .097 .097 .098 .098 .097 .098 .100 .100 .103 .102 .098 .101 .101 .102 .101 .098 .098 .098 .098
Specific Gravity 2.67 2.66 2.64 2.69 2.66 2.69 2.69 2.66 2.67 2.66 2.69 2.70 2.70 2.69 2.70 2.70 2.72 2.71 2.70 2.69 2.71 2.70 2.69 2.72 2.71 2.69 2.70 2.78 2.78 2.84 2.83 2.72 2.81 2.80 2.83 2.81 2.71 2.71 2.71 2.70
IV-37
Table 9 TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q The following typical properties are not guaranteed, since in most cases they are averages for various sizes, product forms and methods of manufacture and may not be exactly representative of any particular product or size. These data TENSILE STRENGTH, ksi
TEMP.
°F
ULTIMATE
YIELD W
ELONGATION IN 2 IN., PERCENT
1100-O
–320 –112 –18 75 212 300 400 500 600 700
25 15 14 13 10 8 6 4 2.9 2.1
6 5.5 5 5 4.6 4.2 3.5 2.6 2 1.6
50 43 40 40 45 55 65 75 80 85
–320 –112 –18 75 212 300 400 500 600 700
30 20 19 18 16 14 10 4 2.9 2.1
20 18 17 17 15 12 7.5 2.6 2 1.6
45 24 20 20 20 23 26 75 80 85
–320 –112 –118 75 212 300 400 500 600 700
34 26 25 24 21 18 6 4 2.9 2.1
26 23 23 22 19 14 3.5 2.6 2 1.6
30 16 15 15 15 20 65 75 80 85
75 212 300 400 500 600 700
55 47 28 16 6.5 3.1 2.3
43 34 19 11 3.8 1.8 1.4
15 16 25 35 45 90 125
–320 –112 –18 75 212 300 400 500 600 700
84 74 72 70 63 40 16 9.5 6.5 4.3
72 65 62 60 57 35 13 7.5 5 3.5
14 13 13 13 15 20 38 52 65 72
–320 –112 –18 75 212 300 400 500 600 700 –320 –112
80 65 64 62 57 40 16 9 6 4.3 85 73
53 42 41 40 39 30 13 7.5 5 3.5 62 52
28 24 23 22 18 15 35 45 65 70 18 17
O T
2011-T3
N
2014-T6, T651
2017-T4, T451
2024-T3 (Sheet)
TEMP.
TENSILE STRENGTH, ksi
ELONGATION IN 2 IN., PERCENT
°F
ULTIMATE
–18 75 212 300 400 500 600 700
72 70 66 55 27 11 7.5 5
51 50 48 45 20 9 6 4
17 17 16 11 23 55 75 100
2024-T4, T351 (plate)
–320 –112 –18 75 212 300 400 500 600 700
84 71 69 68 63 45 26 11 7.5 5
61 49 47 47 45 36 19 9 6 4
19 19 19 19 19 17 27 55 75 100
2024-T6, T651
–320 –112 –18 75 212 300 400 500 600 700
84 72 70 69 65 45 26 11 7.5 5
68 59 58 57 54 36 19 9 6 4
11 10 10 10 10 17 27 55 75 100
2024-T81, T851
–320 –112 –18 75 212 300 400 500 600 700
85 74 73 70 66 55 27 11 7.5 5
78 69 68 65 62 49 20 9 6 4
8 7 7 7 8 11 23 55 75 100
2024-T861
–320 –112 –18 75 212 300 400 500 600 700
92 81 78 75 70 54 21 11 7.5 5
85 77 74 71 67 48 17 9 6 4
5 5 5 5 6 11 28 55 75 100
2117-T4
–320 –112 –18 75 212 300 400 500 600 700
56 45 44 43 36 30 16 7.5 4.7 2.9
33 25 24 24 21 17 12 5.5 3.3 2
30 29 28 27 16 20 35 55 80 110
ES IG D
R
1100-H18
FO
1100-H14
ALLOY AND TEMP
YIELD W
N
ALLOY AND TEMP
are intended only as a basis for comparing alloys and tempers and should not be specified as engineering requirements or used for design purposes.
For all numbered footnotes, see page IV-42.
IV-38
January 2010
Table 9 TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q (Continued)
YIELD W
–452 –320 –112 –18 75 212 300 400 500 600 700
102 86 76 73 70 66 54 27 11 7.5 5.5
90 79 71 68 64 61 49 20 8 6 4.1
10 9 8 8 9 9 13 28 60 75 100
–320 –112 –18 75 212 300 400 500 600 700
72 61 59 59 56 41 22 10 5.5 4
52 45 44 44 42 35 16 6 3 2.5
15 14 13 13 15 17 30 70 85 100
–320 –112 –18 75 212 300 400 500 600 700
73 63 60 58 54 45 34 27 10 4.4
49 44 42 40 37 33 25 20 8 3.7
16 13 12 12 14 17 20 21 40 75
–320 –112 –18 75 212 300 400 500 600 700
83 71 69 66 60 49 36 29 7 4.4
61 54 52 50 47 40 29 23 6 3.7
–320 –12 –18 75 212 300 400 500 600 700
78 67 64 64 62 50 32 13 7.5 5
61 55 54 54 54 44 26 9 4.5 3.5
12 11 10 10 10 14 24 50 80 120
3003-O
–320 –112 –18 75 212 300 400 500 600 700
33 20 17 16 13 11 8.5 6 4 2.8
8.5 7 6.5 6 5.5 5 4.3 3.4 2.4 1.8
46 42 41 40 43 47 60 65 70 70
3003-H14
–320 –112 –18
35 24 22
N
2618-T61
O T
2219-T81, T851
15 13 12 12 15 17 20 21 55 75
25 22 21
TEMP.
°F
TENSILE STRENGTH, ksi
ELONGATION IN 2 IN., PERCENT
75 212 300 400 500 600 700
ULTIMATE 22 21 18 14 7.5 4 2.8
YIELD W 21 19 16 9 4 2.4 1.8
–320 –112 –18 75 212 300 400 500 600 700
41 32 30 29 26 23 14 7.5 4 2.8
33 29 28 27 21 16 9 4 2.4 1.8
23 11 10 10 10 11 18 60 70 70
–320 –112 –18 75 212 300 400 500 600 700
42 28 26 26 26 22 14 10 7.5 5
13 11 10 10 10 10 9.5 7.5 5 3
38 30 26 25 25 35 55 70 80 90
3004-H34
–320 –112 –18 75 212 300 400 500 600 700
52 38 36 35 34 28 21 14 7.5 5
34 30 29 29 29 25 15 7.5 5 3
26 16 13 12 13 22 35 55 80 90
3004-H38
–320 –112 –18 75 212 300 400 500 600 700
58 44 42 41 40 31 22 12 7.5 5
43 38 36 36 36 27 15 7.5 5 3
20 10 7 6 7 15 30 50 80 90
4032-T6
–320 –112 –18 75 212 300 400 500 600 700
66 58 56 55 50 37 13 8 5 3.4
48 46 46 46 44 33 9 5.5 3.2 2
11 10 9 9 9 9 30 50 70 90
3003-H18
ES
3004-O
D
2219-T62
ULTIMATE
ALLOY AND TEMP
R
2218-T61
°F
FO
2124-T851
TEMP.
IG N
TENSILE STRENGTH, ksi
ELONGATION IN 2 IN., PERCENT
ALLOY AND TEMP
16 16 16 20 60 70 70
30 18 16
For all numbered footnotes, see page IV-42.
January 2010
IV-39
Table 9 TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q (Continued)
5052-O
10 8.5 8 8 8 8 7.5 6 4.2 2.6
.. .. .. .. .. .. .. .. .. ..
–320 –112 –18 75 212 300 400 500 600 700
44 30 28 28 28 25 14 9 6 3.9
30 25 24 24 24 22 7.5 6 4.2 2.6
.. .. .. .. .. .. .. .. .. ..
–320 –112 –18 75 212 300 400 500 600 700
46 34 32 32 31 27 14 9 6 3.9
36 30 29 29 29 25 7.5 6 4.2 2.6
.. .. .. .. .. .. .. .. .. ..
–320 –112 –18 75 212 300 400 500 600 700
44 29 28 28 28 23 17 12 7.5 5
16 13 13 13 13 13 11 7.5 5.5 3.1
–320 –112 –18 75 212 300 400 500 600 700
55 40 38 38 38 30 24 12 7.5 5
36 32 31 31 31 27 15 7.5 5.5 3.1
28 21 18 16 18 27 45 80 110 130
5052-H38
–320 –112 –18 75 212 300 400 500 600 700 –320 –112 –18
60 44 42 42 40 34 25 12 7.5 5 59 43 42
44 38 37 37 36 28 15 7.5 5.5 3.1 24 21 21
25 18 15 14 16 24 45 80 110 130 36 30 27
5083-O
42 40 31 22 17 11 6
21 21 19 17 11 7.5 4.2
25 36 50 60 80 110 130
–320 –112 –18 75 212 300 400 500 600 700
55 39 38 38 38 29 22 17 11 6
19 17 17 17 17 16 15 11 7.5 4.2
46 35 32 30 36 50 60 80 110 130
–320 –112 –18 75 212 300 400 500 600 700
52 36 35 35 35 29 22 17 11 6
19 17 17 17 17 16 15 11 7.5 4.2
46 35 32 30 36 50 60 80 110 130
5254-O
–320 –112 –18 75 212 300 400 500 600 700
52 36 35 35 35 29 22 17 11 6
19 17 17 17 17 16 15 11 7.5 4.2
46 35 32 30 36 50 60 80 110 130
5454-O
–320 –112 –18 75 212 300 400 500 600 700
54 37 36 36 36 29 22 17 11 6
19 17 17 17 17 16 15 11 7.5 4.2
39 30 27 25 31 50 60 80 110 130
5454-H32
–320 –112 –18 75 212 300 400 500 600 700
59 42 41 40 39 32 25 17 11 6
36 31 30 30 29 26 19 11 7.5 4.2
32 23 20 18 20 37 45 80 110 130
5086-O
46 35 32 30 36 50 60 80 110 130
°F
ULTIMATE
N
37 22 21 21 21 19 14 9 6 3.9
YIELD W
75 212 300 400 500 600 700
TEMP.
ES IG
–320 –112 –18 75 212 300 400 500 600 700
N
5052-H34
YIELD W
TENSILE STRENGTH, ksi
ELONGATION IN 2 IN., PERCENT
ALLOY AND TEMP
5154-O
D
5050-H38
ULTIMATE
ELONGATION IN 2 IN., PERCENT
R
5050-H34
°F
TENSILE STRENGTH, ksi
FO
5050-O
TEMP.
O T
ALLOY AND TEMP
For all numbered footnotes, see page IV-42.
IV-40
January 2010
Table 9 TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q (Continued)
41 36 35 35 34 28 19 11 7.5 4.2
30 21 18 16 18 32 45 80 110 130
–320 –112 –18 75 212 300 400 500 600 700
62 46 45 45 42 31 22 17 11 6
26 23 23 23 22 20 17 11 7.5 4.2
32 25 22 20 31 50 60 80 110 130
–320 –112 –18 75 212 300 400 500 600 700
44 29 28 28 28 23 17 12 7.5 5
16 13 13 13 13 13 11 7.5 5.5 3.1
46 35 32 30 30 50 60 80 110 130
–320 –112 –18 75 212 300 400 500 600 700
55 40 38 38 38 30 24 12 7.5 5
36 32 31 31 31 27 15 7.5 5.5 3.1
°F
ULTIMATE
YIELD W
75 212 300 400 500 600 700
45 42 34 19 7.5 4.6 3
40 38 31 15 5 2.7 1.8
17 18 20 28 60 85 95
–320 –112 –18 75 212 300 400 500 600 700
34 26 24 22 22 21 9 4.5 3.2 2.3
16 15 14 13 14 15 6.5 3.5 2.5 2
44 36 34 33 18 20 40 75 80 105
–320 –112 –18 75 212 300 400 500 600 700
37 29 28 27 24 20 9 4.5 3.2 2.3
24 22 22 21 20 18 6.5 3.5 2.5 2
28 24 23 22 18 20 40 75 80 105
6063-T6
–320 –112 –18 75 212 300 400 500 600 700
47 38 36 35 31 21 9 4.5 3.3 2.3
36 33 32 31 28 20 6.5 3.5 2.5 2
24 20 19 18 15 20 40 75 80 105
6101-T6
–320 –112 –18 75 212 300 400 500 600 700
43 36 34 32 28 21 10 4.8 3 2.5
33 30 29 28 25 19 7 3.3 2.3 1.8
24 20 19 19 20 20 40 80 100 105
6151-T6
–320 –112 –18 75 212 300 400 500 600 700
57 50 49 48 43 28 14 6.5 5 4
50 46 45 43 40 27 12 5 3.9 3.2
20 17 17 17 17 20 30 50 43 35
6063-T1
6063-T5
28 21 18 16 18 27 45 80 110 130
–320 –112 –18 75 212 300 400 500 600 700
60 44 42 42 40 34 25 12 7.5 5
44 38 37 37 36 28 15 7.5 5.5 3.1
25 18 15 14 16 24 45 80 110 130
6053-T6, T651
75 212 300 400 500 600 700
37 32 25 13 5.5 4 2.9
32 28 24 12 4 2.7 2
13 13 13 25 70 80 90
6061-T6, T651
–320 –112 –18
60 49 47
47 42 41
22 18 17
TEMP.
IG N
63 46 44 44 43 34 26 17 11 6
N
5652-H38
–320 –112 –18 75 212 300 400 500 600 700
O T
5652-H34
YIELD W
TENSILE STRENGTH, ksi
ELONGATION IN 2 IN., PERCENT
ALLOY AND TEMP
ES
5652-O
ULTIMATE
ELONGATION IN 2 IN., PERCENT
D
5456-O
°F
TENSILE STRENGTH, ksi
R
5454-H34
TEMP.
FO
ALLOY AND TEMP
For all numbered footnotes, see page IV-42.
January 2010
IV-41
Table 9 TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q (Continued)
ULTIMATE
YIELD W
ELONGATION IN 2 IN., PERCENT
6262-T651
–320 –112 –18 75 212 300
60 49 47 45 42 34
47 42 41 40 38 31
22 18 17 17 18 20
6262-T9
–320 –112 –18 75 212 300 400 500 600 700
74 62 60 58 53 38 15 8.5 4.6 3
67 58 56 55 52 37 13 6 2.7 1.8
14 10 10 10 10 14 34 48 85 95
92 79 75 73 65 27 13 9 6.5 4.6
9 11 11 11 14 30 55 65 70 70
–320 –112 –18 75 212 300 400 500 600 700
92 79 76 73 63 31 16 11 8 6
72 67 65 63 58 27 13 9 6.5 4.6
14 14 13 13 15 30 55 65 70 70
–320 –112 –18 75 212 300 400 –320 –112
106 90 87 80 72 35 18 106 94
98 83 80 73 69 31 13 94 84
O T
7175-T74
102 90 86 83 70 31 16 11 8 6
N
7178-T6, T651
7178-T76, T7651
7475-T61 Sheet
R
7075-T73, T7351
–320 –112 –18 75 212 300 400 500 600 700
FO
7075-T6, T651
13 14 16 14 17 30 65 5 8
ALLOY AND TEMP
TENSILE STRENGTH, ksi
°F
ULTIMATE
YIELD W
ELONGATION IN 2 IN., PERCENT
–18 75 212 300 400 500 600 700
91 88 73 31 15 11 8.5 6.5
81 78 68 27 12 9 7 5.5
9 11 14 40 70 76 80 80
–320 –112 –18 75 212 300 400 500 600 700
106 91 88 83 69 31 15 11 8.5 6.5
89 78 76 73 64 27 12 9 7 5.5
10 10 10 11 17 40 70 76 80 80
–320 –112 –18 75 212 300 400 500 600 700
99 88 84 80 70 30 14 9.5 6.5 5
87 79 75 72 65 26 11 7 5.5 3.8
10 12 12 12 14 28 55 70 80 85
–320 –112 –18 75 212 300 400 500 600 700
95 84 80 76 64 30 14 9.5 6.5 5
82 73 70 67 61 26 11 7 5.5 3.8
11 12 12 12 14 38 55 70 80 85
TEMP.
N
°F
TENSILE STRENGTH, ksi
ES IG
TEMP.
D
ALLOY AND TEMP
7475-T761
Q These data are based on a limited amount of testing and represent the lowest strength during 10,000 hours of exposure at testing temperature under no load; stress applied at 5,000 psi/min to yield strength and then at strain rate of 0.05 in./in./min to failure. Under some conditions of temperature and time, the application of heat will adversely affect certain other properties of some alloys. W Offset equals 0.2 percent.
IV-42
January 2010
Table 9M TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q The following typical properties are not guaranteed, since in most cases they are averages for various sizes, product forms and methods of manufacture and may not be exactly representative of any particular product or size. These data
ULTIMATE
YIELD W
ELONGATION IN 50 MM PERCENT
–195 –80 –30 25 100 150 205 260 315 370
170 105 95 90 70 55 41 28 20 14
41 38 34 34 32 29 24 18 14 11
50 43 40 40 45 55 65 75 80 85
1100-H14
–195 –80 –30 25 100 150 205 260 315 370
205 140 130 125 110 95 70 28 20 14
140 125 115 115 105 85 50 18 14 11
45 24 20 20 20 23 26 75 80 85
1100-H18
–195 –80 –30 25 100 150 205 260 315 370
235 180 170 165 145 125 41 28 20 14
180 160 160 150 130 95 24 18 14 11
30 16 15 15 15 20 65 75 80 85
25 100 150 205 260 315 370
380 325 195 110 45 21 16
–195 –80 –30 25 100 150 205 260 315 370 –195 –80 –30 25 100 150 205 260 315 370
FO 295 235 130 75 26 12 10
15 16 25 35 45 90 125
580 510 495 485 435 275 110 65 45 30
495 450 425 415 395 240 90 50 34 24
14 13 13 13 15 20 38 52 65 72
550 450 440 425 395 275 110 60 41 30
365 290 285 275 270 205 90 50 34 24
28 24 23 22 18 15 35 45 65 70
O T
2011-T3
N
2014-T6, T651
2017-T4, T451
TEMP.
°C
ULTIMATE
YIELD W
ELONGATION IN 50 MM PERCENT
2024-T3 (Sheet)
–195 –80 –30 25 100 150 205 260 315 370
585 505 495 485 455 380 185 75 50 34
425 360 350 345 330 310 140 60 41 28
18 17 17 17 16 11 23 55 75 100
–195 –80 –30 25 100 150 205 260 315 370
580 490 475 470 435 310 180 75 50 34
420 340 325 325 310 250 130 60 41 28
19 19 19 19 19 17 27 55 75 100
2024-T6, T651
–195 –80 –30 25 100 150 205 260 315 370
580 495 485 475 450 310 180 75 50 34
470 405 400 395 370 250 130 60 41 28
11 10 10 10 10 17 27 55 75 100
2024-T81, T851
–195 –80 –30 25 100 150 205 260 315 370
585 510 505 485 455 380 185 75 50 34
540 475 470 450 425 340 140 60 41 28
8 7 7 7 8 11 23 55 75 100
2024-T861
–195 –80 –30 25 100 150 205 260 315 370
635 560 540 515 485 370 145 75 50 34
585 530 510 490 460 330 115 60 41 28
5 5 5 5 6 11 28 55 75 100
2117-T4
–195 –80 –30 25 100 150 205 260 315 370
385 310 305 295 250 205 110 50 32 20
230 170 165 165 145 115 85 38 23 14
30 29 28 27 16 20 35 55 80 110
2024-T4, T351 (plate)
R
1100-O
TENSILE STRENGTH, MPa
ALLOY AND TEMPER
IG N
°C
TENSILE STRENGTH, MPa
ES
TEMP.
D
ALLOY AND TEMPER
are intended only as a basis for comparing alloys and tempers and should not be specified as engineering requirements or used for design purposes.
For all numbered footnotes, see page IV-47.
January 2010
IV-43
Table 9M TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q (Continued)
°C
ULTIMATE
YIELD W
ELONGATION IN 50 MM PERCENT
2124-T851
–268 –195 –80 –30 25 100 150 205 260 315 370
705 595 525 505 485 455 370 185 75 50 38
620 545 490 470 440 420 340 140 55 41 28
10 9 8 8 9 9 13 28 60 75 100
2218-T61
–195 –80 –30 25 100 150 205 260 315 370
495 420 405 405 385 285 150 70 38 28
360 310 305 305 290 240 110 41 21 17
15 14 13 13 15 17 30 70 85 100
2219-T62
–195 –80 –30 25 100 150 205 260 315 370
505 435 415 400 370 310 235 185 70 30
340 305 290 275 255 230 170 140 55 26
16 13 12 12 14 17 20 21 40 75
2219-T81, T851
–195 –80 –30 25 100 150 205 160 315 370
570 490 475 455 415 340 250 200 48 30
–195 –80 –30 25 100 150 205 260 315 370 –195 –80 –30 25 100 150 205 260 315 370
3003-O
540 460 440 440 425 345 220 90 50 34
420 380 370 370 370 305 180 60 31 24
12 11 10 10 10 14 24 50 80 120
230 140 115 110 90 75 60 41 28 19
60 50 45 41 38 34 30 23 17 12
46 42 41 40 43 47 60 65 70 70
ELONGATION IN 50 MM PERCENT
TEMP.
°C
ULTIMATE
YIELD W
3003-H14
–195 –80 –30 25 100 150 205 260 315 370
240 165 150 150 145 125 95 50 28 19
170 150 145 145 130 110 60 28 17 12
3003-H18
–195 –80 –30 25 100 150 205 260 315 370
285 220 205 200 180 160 95 50 28 19
230 200 195 185 145 110 60 28 17 12
23 11 10 10 10 11 18 60 70 70
–195 –80 –30 25 100 150 205 260 315 370
290 195 180 180 180 150 95 70 50 34
90 75 70 70 70 70 65 50 34 21
38 30 26 25 25 35 55 70 80 90
3004-H34
–195 –80 –30 25 100 150 205 260 315 370
360 260 250 240 235 195 145 95 50 34
235 205 200 200 200 170 105 50 34 21
26 16 13 12 13 22 35 55 80 90
3004-H38
–195 –80 –30 25 100 150 205 260 315 370
400 305 290 285 275 215 150 85 50 34
295 260 250 250 250 185 105 50 34 21
20 10 7 6 7 15 30 50 80 90
–195 –80 –30 25 100 150 205 260 315 370
455 400 385 380 345 255 90 55 34 23
330 315 315 315 305 230 60 38 22 14
11 10 9 9 9 9 30 50 70 90
D
3004-O
R
FO 15 13 12 12 15 17 20 21 55 75
O T
N
2618-T61
420 370 360 345 325 275 200 160 41 26
TENSILE STRENGTH, MPa
ALLOY AND TEMPER
ES IG
TEMP.
N
TENSILE STRENGTH, MPa
ALLOY AND TEMPER
4032-T6
30 18 16 16 16 16 20 60 70 70
For all numbered footnotes, see page IV-47.
IV-44
January 2010
Table 9M TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q (Continued) TENSILE STRENGTH, MPa
°C
ULTIMATE
YIELD W
ELONGATION IN 50 MM PERCENT
.. .. .. .. .. .. .. .. .. ..
5083-O
–195 –80 –30 25 100 150 205 260 315 370
405 295 290 290 275 215 150 115 75 41
165 145 145 145 145 130 115 75 50 29
36 30 27 25 36 50 60 80 110 130
205 170 165 165 165 150 50 41 29 18
.. .. .. .. .. .. .. .. .. ..
5086-O
315 235 220 220 215 185 95 60 41 27
250 205 200 200 200 170 50 41 29 18
.. .. .. .. .. .. .. .. .. ..
–195 –80 –30 25 100 150 205 260 315 370
305 200 195 195 195 160 115 85 50 34
110 90 90 90 90 90 75 50 38 21
–195 –80 –30 25 100 150 205 260 315 370
380 275 260 260 260 205 165 85 50 34
–195 –80 –30 25 100 150 205 260 315 370
415 305 290 290 275 235 170 85 50 34
–195 –80 –30 25 100 150 205 260 315 370
255 150 145 145 145 130 95 60 41 27
70 60 55 55 55 55 50 41 29 18
5050-H34
–195 –80 –30 25 100 150 205 260 315 370
305 205 195 195 195 170 95 60 41 27
5050-H38
–195 –80 –30 25 100 150 205 260 315 370
5052-O
5052-H38
380 270 260 260 260 200 150 115 75 41
130 115 115 115 115 110 105 75 50 29
46 35 32 30 36 50 60 80 110 130
5154-O
–195 –80 –30 25 100 150 205 260 315 370
360 250 240 240 240 200 150 115 75 41
130 115 115 115 115 110 105 75 50 29
46 35 32 30 36 50 60 80 110 130
5254-O
–195 –80 –30 25 100 150 205 260 315 370
360 250 240 240 240 200 150 115 75 41
130 115 115 115 115 110 105 75 50 29
46 35 32 30 36 50 60 80 110 130
250 220 215 215 215 185 105 50 38 21
28 21 18 16 18 27 45 80 110 130
5454-O
–195 –80 –30 25 100 150 205 260 315 370
370 255 250 250 250 200 150 115 75 41
130 115 115 115 115 110 105 75 50 29
39 30 27 25 31 50 60 80 110 130
305 260 255 255 250 195 105 50 38 21
25 18 15 14 16 24 45 80 110 130
5454-H32
–195 –80 –30 25 100 150 205 260 315 370
405 290 285 275 270 220 170 115 75 41
250 215 205 205 200 180 130 75 50 29
32 23 20 18 20 37 45 80 110 130
FO
46 35 32 30 36 50 60 80 110 130
O T
N
5052-H34
–195 –80 –30 25 100 150 205 260 315 370
ES
5050-O
YIELD W
D
ULTIMATE
R
°C
IG N
TEMP.
TEMP.
ELONGATION IN 50 MM PERCENT
TENSILE STRENGTH, MPa
ALLOY AND TEMPER
ALLOY AND TEMPER
For all numbered footnotes, see page IV-47.
January 2010
IV-45
Table 9M TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q (Continued) TENSILE STRENGTH, MPa
ALLOY AND TEMPER
TEMP.
°C
ULTIMATE
YIELD W
ELONGATION IN 50 MM PERCENT
5454-H34
–195 –80 –30 25 100 150 205 260 315 370
435 315 305 305 295 235 180 115 75 41
285 250 240 240 235 195 130 75 50 29
5456-O
–195 –80 –30 25 100 150 205 260 315 370
425 315 310 310 290 215 150 115 75 41
5652-O
–195 –80 –30 25 100 150 205 260 315 370
5652-H34
ULTIMATE
YIELD W
30 21 18 16 18 32 45 80 110 130
6061-T6, T651
–195 –80 –30 25 100 150 205 260 315 370
415 340 325 310 290 235 130 50 32 21
325 290 285 275 260 215 105 34 19 12
180 160 160 160 150 140 115 75 50 29
32 25 22 20 31 50 60 80 110 130
6063-T1
–195 –80 –30 25 100 150 205 260 315 370
235 180 165 150 150 145 60 31 22 16
110 105 95 90 95 105 45 24 17 14
44 36 34 33 18 20 40 75 80 105
305 200 195 195 195 160 115 85 50 34
110 90 90 90 90 90 75 50 38 21
46 35 32 30 30 50 60 80 110 130
–195 –80 –30 25 100 150 205 260 315 370
255 200 195 185 165 140 60 31 22 16
165 150 150 145 140 125 45 24 17 14
28 24 23 22 18 20 40 75 80 105
–195 –80 –30 25 100 150 205 260 315 370
380 275 260 260 260 205 165 85 50 34
250 220 215 215 215 185 105 50 38 21
–195 –80 –30 25 100 150 205 260 315 370
415 305 290 290 275 235 170 85 50 34
25 100 150 205 260 315 370
255 220 170 90 38 28 20
ES IG
N
°C
R
D
6063-T5
22 18 17 17 18 20 28 60 85 95
6063-T6
–195 –80 –30 25 100 150 205 260 315 370
325 260 250 240 215 145 60 31 23 16
250 230 220 215 195 140 45 24 17 14
24 20 19 18 15 20 40 75 80 105
305 260 255 255 250 195 105 50 38 21
25 18 15 14 16 24 45 80 110 130
6101-T6
–195 –80 –30 25 100 150 205 260 315 370
295 250 235 220 195 145 70 33 21 17
230 205 200 195 170 130 48 23 16 12
24 20 19 19 20 20 40 80 100 105
220 195 165 85 28 19 14
13 13 13 25 70 80 90
6151-T6
–195 –80 –30 25 100 150 205 260 315 370
395 345 340 330 295 195 95 45 34 28
345 315 310 295 275 185 85 34 27 22
20 17 17 17 17 20 30 50 43 35
FO
28 21 18 16 18 27 45 80 110 130
O T
6053-T6, T651
ELONGATION IN 50 MM PERCENT
TEMP.
N
5652-H38
TENSILE STRENGTH, MPa
ALLOY AND TEMPER
For all numbered footnotes, see page IV-47.
IV-46
January 2010
Table 9M TYPICAL TENSILE PROPERTIES AT VARIOUS TEMPERATURES Q (Continued) ELONGATION IN 50 MM PERCENT
ULTIMATE
YIELD W
6262-T651
–195 –80 –30 25 100 150
415 340 325 310 290 235
325 290 285 275 260 215
22 18 17 17 18 20
6262-T9
–195 –80 –30 25 100 150 205 260 315 370
510 425 415 400 365 260 105 60 32 21
460 400 385 380 360 255 90 41 19 12
14 10 10 10 10 14 34 48 85 95
–195 –80 –30 25 100 150 205 260 315 370
705 620 595 570 485 215 110 75 55 41
635 545 515 505 450 185 90 60 45 32
9 11 11 11 14 30 55 65 70 70
–195 –80 –30 25 100 150 205 260 315 370
635 545 525 505 435 215 110 75 55 41
495 460 450 435 400 185 90 60 45 32
14 14 13 13 15 30 55 65 70 70
–195 –80 –30 25 100 150 205
730 620 600 550 495 240 125
7075-T73, T7351
675 570 550 505 475 215 90
O T
7175-T74
FO
7075-T6, T651
7178-T6, T651
7178-T76, T7651
7475-T61 Sheet
R
°C
13 14 16 14 17 30 65
ALLOY AND TEMPER
TEMP.
TENSILE STRENGTH, MPa
°C
ULTIMATE
YIELD W
–195 –80 –30 25 100 150 205 260 315 370
730 650 625 605 505 215 105 75 60 45
650 580 560 540 470 185 85 60 48 38
IG N
TENSILE STRENGTH, MPa
7475-T761 Sheet
ELONGATION IN 50 MM PERCENT 5 8 9 11 14 40 70 76 80 80
–195 –80 –30 25 100 150 205 260 315 370
730 625 605 570 475 215 105 75 60 45
615 540 525 505 440 185 85 60 48 38
10 10 10 11 17 40 70 76 80 80
–195 –80 –30 25 100 150 205 260 315 370
685 605 580 550 485 205 95 65 45 34
600 545 515 495 450 180 75 50 38 26
10 12 12 12 14 28 55 70 80 85
–195 –80 –30 25 100 150 205 260 315 370
655 580 550 525 440 205 95 65 45 34
565 505 485 460 420 180 75 50 38 26
11 12 12 12 14 38 55 70 80 85
ES
TEMP.
D
ALLOY AND TEMPER
N
Q These data are based on a limited amount of testing and represent the lowest strength during 10,000 hours of exposure at testing temperature under no load; stress applied at 5,000 psi/min to yield strength and then at strain rate of 0.05 in./in./min to failure. Under some conditions of temperature and time, the application of heat will adversely affect certain other properties of some alloys. W Offset equals 0.2 percent.
January 2010
IV-47
Aluminum Design Manual
PART V Section Properties
V Section Properties TABLE OF CONTENTS Table 1 Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11 Table 12 Table 13 Table 14 Table 15 Table 16 Table 17 Table 18 Table 19 Table 20 Table 21 Table 22 Table 23 Table 24 Table 25 Table 26 Table 27 Table 28
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Section Designations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Weights Per Square Foot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Aluminum Association Standard Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 American Standard Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Car and Shipbuilding Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Canadian Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Aluminum Association Standard I Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Wide Flange Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 Wide Flange Beams—Army-Navy Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 American Standard I Beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Canadian I Beams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Canadian Wide Flange Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Angles—Equal Legs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 Square End Angles—Equal Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Angles—Unequal Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 Square End Angles—Unequal Legs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 Tees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Army-Navy and Special Tees. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Zees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 Round Tubes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Pipes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Square Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Rectangular Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 Roofing and Siding—Dimensions and Weights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Roofing and Siding—Section Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 Decimal Equivalents in Inches of Sheet Metal and Wire Gauges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 Geometric Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
January 2010
V-3
Table 1 NOMENCLATURE Symbol
Property
A
area
Units in2
b
width
in.
Cw
warping constant
in6
d
depth
in.
I
moment of inertia
in4
J
torsion constant
in4
r
radius of gyration
in.
r0
polar radius of gyration about the shear center
in.
R
fillet radius
in.
Rb
mid-thickness radius of a pipe or tube
in.
S
section modulus
in3
t
thickness
in.
tf
flange thickness
in.
tw
web thickness
in.
Wt
weight per unit length
lb/ft
x
location of the major axis
in.
x0
x coordinate of shear center
in.
y
location of the minor axis
in.
y0
y coordinate of shear center
in.
x and y subscripts denote the axis about which the property is taken. The x axis is the major axis. The y axis is the minor axis.
V-4
January 2010
Table 2 SECTION DESIGNATIONS Section
Designation
Example
Description
Channels
CS Depth × Wt
CS 4 × 2.33
C shapes with flat flanges; includes Canadian Channels
Car and Shipbuilding Channels
CS Depth × Wt
CS 3 × 2.23
C shapes; some have flanges with a slope on the inner surface
American Standard Channels
C Depth × Wt
C 2 × 1.22
C shapes with flanges with a 1:6 slope on the inner surface
I-Beams
I Depth × Wt
I 12 × 11.7
I shapes with flat flanges; includes Canadian I-Beams
American Standard I-Beams
S Depth × Wt
S 10 × 12.1
I shapes with flanges with a 1:6 slope on the inner surface
Wide Flange Beams
WF Nominal Depth × Wt
WF 12 × 13.8
I shapes with a flange width approximately equal to the depth
Army-Navy Wide Flange Beams
WF(A-N) Depth × Wt
WF(A-N) 4 × 4.14
I shapes with flat flanges and a radius on the inside corner of the flanges
Angles
L long leg × short leg × thickness
L3×2×¼
L shaped product with a fillet at the junction of the legs and radii on the inside tips of the legs
Square End Angles
LS long leg × short leg × thickness
LS 3 × 3 × ¹⁄8
L shaped product with small radii at the corners
Tees
T Depth × Width × Wt
T 2.50 × 2.50 × 1.91
T shapes
Zees
Z Depth × Width × Wt
Z 4.00 × 3.19 × 4.32
Z shapes
Plates
PL Thickness × Width
PL 0.375 × 60
Rolled product with a rectangular cross section at least 0.25 in. thick
Rods
RD Diameter
RD 0.500
Solid product with a circular cross section at least 0.375 in. in diameter
Square Bars
SQ Side dimension
SQ 4
Solid product with a square cross section at least 0.375 in. on a side
Pipes
NPS size × SCH schedule no.
NPS 4 × SCH 40
Tube in standardized outside diameters and wall thicknesses
Round Tubes
Outside diameter OD × wall thickness WALL
4 OD × 0.125 WALL
Hollow product with a circular cross section
Rectangular Tubes
RT short side × long side × wall thickness
RT 4 × 6 × ¼
Hollow product with a rectangular cross section (including square tube)
January 2010
V-5
Table 3 WEIGHTS PER SQUARE FOOT The weight per square foot for an alloy with density of 0.100 lb/in3 is shown for each thickness. The weights for other alloys can be calculated using the density given in Part IV Table 8. Commonly used thicknesses are shown BOLD. Thickness (in.) Decimal
Thickness (in.) Weight (lb/ft2)
Decimal
.006
0.086
.132
.007
0.101
.140
.008
0.115
.150
.009
0.130
.010
0.144
.011
Fraction
Weight (lb/ft2)
1.90
1.625
5
1 /8
23.40
2.02
1.750
1¾
25.20
2.16
1.875
1 7/8
27.00
.160
2.30
2.000
2
28.80
.170
2.45
2.125
2 1/8
30.60
0.158
.180
2.59
2.250
2¼
32.40
.012
0.173
.1875
2.70
2.375
2 3/8
34.20
.013
0.187
.190
2.74
2.500
2½
36.00
.014
0.202
.200
2.88
2.625
2 5/8
37.80
0.230
.212
3.05
2.750
2¾
39.60
.018
0.259
.224
3.23
2.875
2 7/8
41.40
/64
1
/16
3
.019
0.274
.236
.020
0.288
.250
.021
0.302
.266
17
.022
0.317
.281
9
.024
0.346
.297
19
.025
0.360
.313
5
.026
0.374
.328
21
.028
0.403
.344
11
.030
0.432
.359
23
.032
0.461
.375
3
.034
0.490
.391
25
.036
0.518
.406
13
.038
0.547
.422
27
3.40
3.000
3
43.20
3.60
3.250
3¼
46.80
/64
3.83
3.500
3½
50.40
/32
4.05
3.750
3¾
54.00
/64
4.28
4.000
4
57.60
/16
4.51
4.250
4¼
61.20
/64
4.72
4.500
4½
64.80
/32
4.95
4.750
4¾
68.40
/64
5.17
5.000
5
72.00
/8
5.40
5.250
5¼
75.60
/64
5.63
5.500
5½
79.20
/32
5.85
5.750
5¾
82.80
/64
6.08
6.000
6
86.40
/16
6.31
.040
0.576
.438
.042
0.605
.453
29
.045
0.648
.469
15
.048
0.691
.484
31
.050
0.720
.500
.053
0.763
.531
.056
0.806
.562
9
.060
0.864
.594
19
0.907
.625
5
.067
0.965
.656
21
.071
1.02
.688
11
.075
1.08
.719
23
.080
1.15
.750
.085
1.22
.812
13
.090
1.30
.875
7
.095
1.37
.938
15
.100
1.44
1.000
.106
1.53
.112
1.61
/16
1
.118 .125
/8
1
Weight (lb/ft2)
¼
7
.063
V-6
Fraction
Thickness (in.) Decimal
.016
Fraction
/64
6.52
/32
6.75
/64
6.97
½
7.20
/32
7.65
17
/16
8.09
/32
8.55
/8
9.00
/32
9.45
/16
9.91
/32
10.35
¾
10.80
/16
11.69
/8
12.60
/16
13.51
1
14.40
1.125
1
1 /8
16.20
1.250
1¼
18.00
1.70
1.375
1 3/8
19.80
1.80
1.500
1½
21.60
January 2010
January 2010
V-7
5.000
6.000
2.000
3.000
3.000
4.000
4.000
5.000
5.000
6.000
6.000
7.000
7.000
8.000
8.000
9.000
9.000
10.000
10.000
12.000
12.000
CS 2 × 0.577
CS 2 × 1.07
CS 3 × 1.14
CS 3 × 1.60
CS 4 × 1.74
CS 4 × 2.33
CS 5 × 2.21
CS 5 × 3.09
CS 6 × 2.83
CS 6 × 4.03
CS 7 × 3.21
CS 7 × 4.72
CS 8 × 4.15
CS 8 × 5.79
CS 9 × 4.98
CS 9 × 6.97
CS 10 × 6.14
CS 10 × 8.36
CS 12 × 8.27
CS 12 × 11.8
CS 14 × 13.91 14.000
0.640
0.620
0.470
0.500
0.410
0.440
0.350
0.410
0.350
0.380
0.290
0.350
0.290
0.320
0.260
0.290
0.230
0.260
0.200
0.260
0.130
Flange Thickness tf in.
0.320
0.350
0.290
0.310
0.250
0.290
0.230
0.250
0.190
0.210
0.170
0.210
0.170
0.190
0.150
0.190
0.150
0.170
0.130
0.170
0.130
Web Thickness tw in.
0.450
0.450
0.400
0.400
0.350
0.350
0.350
0.350
0.300
0.300
0.300
0.300
0.300
0.300
0.300
0.250
0.250
0.250
0.250
0.150
0.100
Fillet Radius R in.
11.8
10.1
7.04
7.11
5.22
5.93
4.24
4.92
3.53
4.01
2.73
3.43
2.41
2.63
1.88
1.98
1.48
1.36
0.965
0.911
0.490
Area A in2
1. New shape; check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
4.000
4.250
3.500
4.000
3.250
3.750
3.000
3.500
2.750
3.250
2.500
2.750
2.250
2.250
2.000
1.750
1.500
1.250
1.000
2.000
Designation
Width b in.
Depth d in.
401
240
160
116
83.2
78.3
54.4
52.7
37.4
33.8
22.1
21.0
14.4
11.1
7.88
5.21
3.91
1.97
1.41
0.546
0.288
Ix in4
57.3
39.9
26.6
23.2
16.6
17.4
12.1
13.2
9.35
9.65
6.31
7.01
4.78
4.45
3.15
2.60
1.95
1.31
0.940
0.546
0.288
Sx in3
Axis x-x
5.82
4.88
4.77
4.04
3.99
3.63
3.58
3.27
3.26
2.90
2.85
2.48
2.44
2.06
2.05
1.62
1.63
1.20
1.21
0.774
0.766
rx in.
44.7
25.7
11.0
13.0
6.33
9.60
4.40
7.12
3.25
5.13
2.10
3.76
1.53
2.05
0.975
1.02
0.601
0.417
0.217
0.139
0.0450
Iy in4
11.2
7.59
3.85
4.46
2.55
3.49
1.89
2.82
1.57
2.23
1.10
1.76
0.896
1.14
0.642
0.692
0.446
0.368
0.215
0.178
0.0639
Sy in3
ry in.
1.94
1.60
1.25
1.35
1.10
1.27
1.02
1.20
0.959
1.13
0.878
1.05
0.798
0.884
0.720
0.717
0.638
0.554
0.474
0.390
0.303
Axis y-y
Table 4 ALUMINUM ASSOCIATION STANDARD CHANNELS
2.00
1.61
1.14
1.34
1.02
1.25
0.928
1.22
0.934
1.20
0.842
1.12
0.788
0.955
0.731
0.775
0.653
0.617
0.494
0.471
0.296
x in.
xo in.
4.25
3.40
2.47
2.84
2.20
2.68
2.02
2.59
1.99
2.52
1.81
2.34
1.67
1.98
1.54
1.60
1.38
1.25
1.02
0.904
0.626
X
shear center
xo
1510
639
281
226
111
135
62.8
78.5
36.0
43.0
17.8
23.1
9.52
8.70
4.17
2.76
1.65
0.626
0.332
0.0894
0.0324
Cw in6
J in4
R
tw
x
1.19
0.948
0.367
0.444
0.209
0.293
0.127
0.210
0.102
0.147
0.0552
0.109
0.0495
0.0700
0.0314
0.0444
0.0202
0.0246
0.00990
0.0171
0.00274
Y
Y
b
X
7.46
6.16
5.51
5.12
4.69
4.69
4.24
4.34
3.94
4.01
3.49
3.57
3.06
2.99
2.66
2.39
2.22
1.82
1.65
1.25
1.03
r0 in.
tf
d
V-8
January 2010
Depth d in. 2.000
3.000 3.000 3.000
4.000 4.000 4.000
5.000 5.000 5.000
6.000 6.000 6.000 6.000
7.000 7.000 7.000 7.000
Designation C 2 × 1.22
C 3 × 1.42 C 3 × 1.73 C 3 × 2.07
C 4 × 1.85 C 4 × 2.16 C 4 × 2.50
C 5 × 2.32 C 5 × 3.11 C 5 × 3.97
C 6 × 2.83 C 6 × 3.00 C 6 × 3.63 C 6 × 4.50
C 7 × 3.54 C 7 × 4.23 C 7 × 5.10 C 7 × 5.96
2.110 2.194 2.299 2.404
1.920 1.945 2.034 2.157
1.750 1.885 2.032
1.580 1.647 1.720
1.410 1.498 1.596
Width b in. 1.410
0.210 0.210 0.210 0.210
0.200 0.200 0.200 0.200
0.190 0.190 0.190
0.180 0.180 0.180
0.170 0.170 0.170
Flange Tip Thickness tf in. 0.170
0.367 0.367 0.367 0.367
0.343 0.343 0.343 0.343
0.320 0.320 0.320
0.297 0.297 0.297
0.273 0.273 0.273
Average Flange Thickness t in. 0.273
0.230 0.314 0.419 0.524
0.200 0.225 0.314 0.438
0.190 0.325 0.472
0.180 0.247 0.320
0.170 0.258 0.356
Web Thickness tw in. 0.170
0.310 0.310 0.310 0.310
0.300 0.300 0.300 0.300
0.290 0.290 0.290
0.280 0.280 0.280
0.270 0.270 0.270
Fillet Radius R1 in. 0.270
0.130 0.130 0.130 0.130
0.120 0.120 0.120 0.120
0.110 0.110 0.110
0.110 0.110 0.110
0.100 0.100 0.100
Tip Radius R2 in. 0.100
5.50 5.50 5.50 5.50
4.50 4.50 4.50 4.50
3.75 3.75 3.75
2.75 2.75 2.75
1.75 1.75 1.75
d1 in. 0.75
3.01 3.60 4.33 5.07
2.40 2.55 3.09 3.83
1.97 2.64 3.38
1.57 1.84 2.13
1.21 1.47 1.76
Area A in2 1.04
21.8 24.2 27.2 30.3
13.1 13.6 15.2 17.4
7.49 8.90 10.4
3.83 4.19 4.58
1.66 1.85 2.07
Ix in4 0.622
Table 5 AMERICAN STANDARD CHANNELS
6.24 6.93 7.78 8.64
4.37 4.52 5.06 5.80
3.00 3.56 4.17
1.92 2.10 2.29
1.10 1.24 1.38
Sx in3 0.622
Axis x-x
2.69 2.60 2.51 2.44
2.34 2.31 2.22 2.13
1.95 1.83 1.76
1.56 1.51 1.47
1.17 1.12 1.08
rx in. 0.774
1.01 1.17 1.38 1.59
0.69 0.73 0.87 1.05
0.48 0.63 0.81
0.32 0.37 0.43
0.20 0.21 0.31
Iy in4 0.172
0.64 0.70 0.78 0.86
0.49 0.51 0.56 0.64
0.38 0.45 0.53
0.28 0.31 0.34
0.20 0.21 0.27
Sy in3 0.188
Axis y-y
0.58 0.57 0.56 0.56
0.54 0.54 0.50 0.52
0.49 0.49 0.49
0.45 0.45 0.45
0.40 0.41 0.42
ry in. 0.407
0.54 0.52 0.53 0.55
0.51 0.51 0.50 0.51
0.48 0.48 0.51
0.46 0.45 0.46
0.44 0.44 0.46
y-axis Location x in. 0.49
January 2010
V-9
8.000 8.000 8.000 8.000
9.000 9.000 9.000 9.000
10.000 10.000 10.000 10.000
12.000 12.000 12.000 12.000
15.000 15.000
Designation
C 8 × 4.25 C 8 × 4.75 C 8 × 5.62 C 8 × 6.48
C 9 × 4.60 C 9 × 5.19 C 9 × 6.91 C 9 × 8.65
C 10 × 5.28 C 10 × 6.91 C 10 × 8.64 C 10 × 10.4
C 12 × 7.41 C 12 × 8.64 C 12 × 10.4 C 12 × 12.1
C 15 × 11.7 C 15 × 17.3
3.400 3.716
2.960 3.047 3.170 3.292
2.600 2.739 2.886 3.033
2.430 2.485 2.648 2.812
2.290 2.343 2.435 2.527
Width b in.
0.400 0.400
0.280 0.280 0.280 0.280
0.240 0.240 0.240 0.240
0.230 0.230 0.230 0.230
0.220 0.220 0.220 0.220
0.650 0.650
0.502 0.502 0.502 0.502
0.437 0.437 0.437 0.437
0.413 0.413 0.413 0.413
0.390 0.390 0.390 0.390
Average Flange Thickness t in.
0.400 0.716
0.300 0.387 0.510 0.632
0.240 0.379 0.526 0.673
0.230 0.285 0.448 0.612
0.250 0.303 0.395 0.487
Web Thickness tw in.
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
Flange Tip Thickness tf in.
0.500 0.500
0.380 0.380 0.380 0.380
0.340 0.340 0.340 0.340
0.330 0.330 0.330 0.330
0.320 0.320 0.320 0.320
Fillet Radius R1 in.
0.240 0.240
0.170 0.170 0.170 0.170
0.140 0.140 0.140 0.140
0.140 0.140 0.140 0.140
0.130 0.130 0.130 0.130
Tip Radius R2 in.
12.4 12.4
10.0 10.0 10.0 10.0
8.25 8.25 8.25 8.25
7.25 7.25 7.25 7.25
6.25 6.25 6.25 6.25
d1 in.
9.96 14.7
6.30 7.35 8.82 10.3
4.49 5.88 7.35 8.82
3.91 4.41 5.88 7.35
3.62 4.04 4.78 5.51
Area A in2
315 404
132 144 162 180
67.4 79.0 91.2 104
47.7 51.0 60.9 70.9
33.9 36.1 40.0 44.0
Ix in4
42.0 53.8
22.0 24.1 27.0 29.9
13.5 15.8 18.2 20.7
10.6 11.3 13.5 15.8
8.46 9.03 10.0 11.0
Sx in3
Axis x-x
5.62 5.24
4.57 4.43 4.29 4.18
3.87 3.66 3.52 3.43
3.49 3.40 3.22 3.11
3.06 2.99 2.90 2.82
rx in.
8.13 11.0
3.99 4.47 5.14 5.82
2.28 2.81 3.36 3.95
1.75 1.93 2.42 2.94
1.40 1.53 1.75 1.98
Iy in4
3.11 3.78
1.76 1.89 2.06 2.24
1.16 1.32 1.48 1.66
0.96 1.01 1.17 1.34
0.81 0.85 0.93 1.01
Sy in3
Axis y-y
0.90 0.87
0.80 0.78 0.76 0.75
0.71 0.69 0.68 0.67
0.67 0.66 0.64 0.63
0.62 0.61 0.61 0.60
ry in.
0.79 0.80
0.69 0.67 0.67 0.69
0.63 0.61 0.62 0.65
0.60 0.59 0.58 0.61
0.56 0.55 0.55 0.57
y-axis Location x in.
V-10
January 2010
3.000 3.000
4.000 5.000
6.000 6.000
8.000 8.000
10.000 10.000 10.000
Designation
CS 3 × 2.23 CS 3 × 2.70
CS 4 × 3.32 CS 5 × 5.82
CS 6 × 5.77 CS 6 × 5.93
CS 8 × 6.59 CS 8 × 7.86
CS 10 × 8.58 CS 10 × 9.32 CS 10 × 10.1 3.500 3.563 3.625
3.000 3.500
3.000 3.500
2.500 2.875
2.000 2.000
Width b in.
0.544 0.544 0.544
0.468 0.524
0.375 0.442
0.344 0.562
0.320 0.375
Avg Flange Thickness tf in.
0.375 0.438 0.500
0.380 0.425
0.500 0.375
0.318 0.438
0.250 0.375
Web Thickness tw in.
1:9 1:9 1:9
1:14.43 1:28.5
0 1:49.6
1:34.9 1:9.8
1:12.1 0
Flange Slope
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
0.625 0.625 0.625
0.550 0.525
0.375 0.480
0.375 0.250
0.250 0.188
Fillet Radius R1 in.
0.188 0.188 0.188
0.220 0.375
0.250 0.420
0.125 0.094
0 0.375
Tip Radius R2 in.
7.50 7.50 7.50
5.75 5.75
4.50 4.00
2.38 3.00
1.75 0.875
d1 in.
7.30 7.93 8.55
5.60 6.68
4.91 5.04
2.82 4.95
1.90 2.30
Area A in2
Ix in.4
110 115 120
54.2 63.8
24.1 28.2
6.84 18.1
2.61 2.89
Table 6 CAR AND SHIPBUILDING CHANNELS
21.9 24.0 24.0
13.5 15.9
8.02 9.41
3.42 7.25
1.74 1.92
Sx in.3
Axis x-x
3.88 3.81 3.75
3.11 3.09
2.21 2.37
1.56 1.91
1.17 1.12
rx in.
7.19 7.73 8.25
4.10 7.06
3.52 5.58
1.62 3.57
0.68 0.78
Iy in.4
2.80 2.93 3.04
1.88 2.84
1.61 2.31
0.95 1.87
0.52 0.59
Sy in.3
0.99 0.99 0.98
0.86 1.03
0.85 1.05
0.76 0.85
0.60 0.58
ry in.
Axis y-y
0.93 0.92 0.91
0.81 1.01
0.81 1.09
0.81 0.96
0.68 0.67
x in.
January 2010
V-11
2.000 2.250
3.000 3.000 3.000
4.000 4.000 4.000 4.000 4.000
5.000 5.000 5.000 5.000
6.000 6.000 6.000
7.000 7.000
8.000 8.000
10.000 10.000 10.000
12.000
Designation
CS 2 × 0.706 CS 2.25 × 0.86
CS 3 × 1.48 CS 3 × 1.85 CS 3 × 2.18
CS 4 × 1.90 CS 4 × 2.24 CS 4 × 2.02 CS 4 × 2.53 CS 4 × 2.90
CS 5 × 2.51 CS 5 × 3.11 CS 5 × 3.05 CS 5 × 3.55
CS 6 × 3.60 CS 6 × 3.51 CS 6 × 6.42
CS 7 × 3.90 CS 7 × 4.61
CS 8 × 4.65 CS 8 × 5.56
CS 10 × 6.23 CS 10 × 7.58 CS 10 × 19.0
CS 12 × 10.3
4.000
3.000 3.500 4.000
2.750 3.000
2.500 3.000
2.000 2.500 3.500
2.000 2.000 2.500 2.500
1.620 1.750 2.000 2.000 2.500
1.500 1.500 2.000
1.500 1.000
Width b in.
0.562
0.437 0.500 1.250
0.375 0.437
0.375 0.375
0.375 0.312 0.500
0.312 0.343 0.312 0.375
0.281 0.281 0.250 0.312 0.312
0.250 0.312 0.312
0.125 0.188
Flange Thickness tf in.
0.375
0.281 0.312 0.812
0.250 0.281
0.218 0.250
0.281 0.250 0.375
0.188 0.281 0.218 0.250
0.188 0.250 0.188 0.250 0.250
0.188 0.250 0.250
0.125 0.188
Web Thickness tw in.
0.625
0.500 0.562 0.500
0.437 0.500
0.437 0.500
0.437 0.437 0.437
0.375 0.375 0.437 0.437
0.375 0.375 0.375 0.375 0.375
0.312 0.312 0.188
0.125 0.062
Fillet Radius R in.
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
8.74
5.29 6.44 16.2
3.96 4.73
3.32 3.92
3.06 2.99 5.46
2.13 2.64 2.60 3.02
1.62 1.90 1.72 2.15 2.46
1.26 1.57 1.86
0.600 0.730
Area A in2
192
79.9 101 223
39.0 47.3
25.8 30.8
15.8 16.4 30.9
8.45 9.59 10.5 12.0
3.95 4.41 4.36 5.21 6.27
1.72 2.03 2.56
0.391 0.505
Ix in4
32.0
16.0 20.1 44.5
9.74 11.8
7.37 8.79
5.26 5.47 10.3
3.38 3.84 4.18 4.79
1.98 2.21 2.18 2.60 3.14
1.15 1.35 1.71
0.391 0.449
Sx in3
Axis x-x
4.69
3.89 3.95 3.71
3.14 3.16
2.79 2.80
2.27 2.34 2.38
1.99 1.90 2.01 1.99
1.56 1.52 1.59 1.56 1.60
1.17 1.14 1.17
0.807 0.832
rx in.
Table 7 CANADIAN CHANNELS
13.1
4.39 7.59 23.3
2.83 4.10
2.02 3.47
1.06 1.74 6.62
0.832 0.942 1.60 1.86
0.396 0.514 0.667 0.810 1.52
0.268 0.321 0.730
0.137 0.062
Iy in4
4.56
2.01 3.07 8.94
1.44 1.95
1.16 1.67
0.740 0.978 2.87
0.607 0.669 0.944 1.11
0.355 0.417 0.486 0.595 0.919
0.265 0.322 0.568
0.136 0.090
Sy in3
1.22
0.911 1.09 1.20
0.846 0.931
0.781 0.941
0.588 0.764 1.10
0.625 0.597 0.786 0.784
0.495 0.520 0.623 0.613 0.786
0.461 0.452 0.627
0.477 0.292
ry in.
Axis y-y
1.13
0.819 1.03 1.39
0.781 0.900
0.759 0.921
0.569 0.719 1.19
0.630 0.592 0.801 0.830
0.504 0.519 0.627 0.638 0.842
0.489 0.502 0.714
0.493 0.303
x in.
X
2.38
1.73 2.15 2.49
1.65 1.87
1.57 1.94
1.13 1.52 2.44
1.29 1.20 1.67 1.69
1.01 1.05 1.31 1.30 1.74
0.981 0.971 1.44
1.06 0.605
xo in.
shear center
xo
J in4
R
tw
x
338
79.3 134 402
32.2 46.1
17.3 29.5
7.04 11.2 40.3
3.59 4.27 6.86 7.89
1.11 1.49 1.84 2.25 4.13
0.415 0.501 1.09
0.665
0.234 0.383 6.547
0.134 0.220
0.109 0.138
0.109 0.079 0.380
0.050 0.086 0.066 0.110
0.032 0.044 0.029 0.058 0.068
0.021 0.043 0.053
0.0938 0.0031 0.0589 0.0086
Cw in6
Y
Y
b
X
5.40
4.35 4.63 4.62
3.65 3.79
3.29 3.53
2.61 2.90 3.58
2.45 2.33 2.73 2.73
1.92 1.92 2.15 2.12 2.49
1.59 1.56 1.96
1.42 1.07
r0 in.
tf
d
V-12
January 2010
3.000 3.000 4.000 4.000
5.000 6.000 6.000 7.000
8.000 8.000 9.000
10.000 10.000 12.000 12.000
14.000
Designation
I 3 × 1.64 I 3 × 2.03 I 4 × 2.31 I 4 × 2.79
I 5 × 3.70 I 6 × 4.03 I 6 × 4.69 I 7 × 5.80
I 8 × 6.18 I 8 × 7.02 I 9 × 8.36
I 10 × 8.65 I 10 × 10.3 I 12 × 11.7 I 12 × 14.3
I 14 × 16.01
8.000
6.000 6.000 7.000 7.000
5.000 5.000 5.500
3.500 4.000 4.000 4.500
2.500 2.500 3.000 3.000
Width b in.
0.600
0.410 0.500 0.470 0.620
0.350 0.410 0.440
0.320 0.290 0.350 0.380
0.200 0.260 0.230 0.290
Flange Thickness tf in.
0.300
0.250 0.290 0.290 0.310
0.230 0.250 0.270
0.190 0.190 0.210 0.230
0.130 0.150 0.150 0.170
Web Thickness tw in.
0.400
0.400 0.400 0.400 0.400
0.300 0.300 0.300
0.300 0.300 0.300 0.300
0.250 0.250 0.250 0.250
Fillet Radius R in.
1. New shape; check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
14.2
7.35 8.75 9.92 12.2
5.26 5.97 7.11
3.15 3.43 3.99 4.93
1.39 1.73 1.96 2.38
Area A in2
489
132 156 256 317
59.7 67.8 102
13.9 22.0 25.5 42.9
2.24 2.71 5.62 6.71
Ix in4
69.9
26.4 31.2 42.6 52.9
14.9 16.9 22.7
5.58 7.33 8.50 12.3
1.49 1.81 2.81 3.36
Sx in3
Axis x-x
6.00
4.24 4.22 5.07 5.11
3.37 3.37 3.79
2.11 2.53 2.53 2.95
1.27 1.25 1.69 1.68
rx in.
51.2
14.8 18.0 26.9 35.5
7.30 8.55 12.2
2.29 3.10 3.74 5.78
0.522 0.679 1.04 1.31
Iy in4
Table 8 ALUMINUM ASSOCIATION STANDARD I-BEAMS
12.8
4.93 6.01 7.69 10.1
2.92 3.42 4.44
1.31 1.55 1.87 2.57
0.418 0.543 0.691 0.872
Sy in3
Axis y-y
1.94
1.42 1.44 1.65 1.71
1.18 1.20 1.31
0.853 0.951 0.968 1.08
0.613 0.627 0.727 0.742
ry in.
2300
340 407 894 1149
107 123 224
12.5 25.3 29.8 63.3
1.02 1.27 3.68 4.50
Cw in6
1.31
0.360 0.620 0.621 1.26
0.188 0.286 0.386
0.0984 0.0888 0.145 0.206
0.0192 0.0374 0.0333 0.0608
J in4
6.31
4.47 4.46 5.33 5.39
3.57 3.57 4.01
2.27 2.71 2.71 3.14
1.41 1.40 1.84 1.84
r0 in.
January 2010
V-13
2.000 4.000 5.000
6.000 6.000 6.000 6.000 6.000
8.000 8.000 8.000 8.000 8.000 8.000
9.750 9.900
11.940 12.060
Designation
WF 2 × 1.43 WF 4 × 4.76 WF 5 × 6.49
WF 6 × 4.16 WF 6 × 5.40 WF 6 × 7.85 WF 6 × 8.30 WF 6 × 9.18
WF 8 × 5.90 WF 8 × 8.32 WF 8 × 10.7 WF 8 × 11.2 WF 8 × 11.8 WF 8 × 13.0
WF 10 × 11.4 WF 10 × 7.30
WF 12 × 13.8 WF 12 × 18.3 8.000 10.000
7.964 5.750
5.250 6.500 8.000 7.940 8.000 8.130
4.000 6.000 5.930 6.000 6.130
2.000 4.000 5.000
Width b in.
0.516 0.576
0.433 0.340
0.308 0.398 0.433 0.458 0.458 0.458
0.279 0.269 0.451 0.451 0.451
0.232 0.370 0.415
Avg Flange Thickness tf in.
0.294 0.345
0.292 0.240
0.230 0.245 0.288 0.313 0.375 0.500
0.230 0.240 0.250 0.313 0.438
0.188 0.313 0.313
Web Thickness tw in.
0 0
0 0
0 0 0 1:18.9 1:18.9 1:18.9
0 0 1:15.6 1:15.6 1:15.6
1:11.4 1:11.3 1:13.6
Flange Slope
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
0.600 0.600
0.500 0.312
0.320 0.400 0.400 0.313 0.313 0.313
0.250 0.250 0.313 0.313 0.313
0.188 0.313 0.313
Fillet Radius R1 in.
0 0
0 0
0 0 0 0.179 0.179 0.179
0 0 0.180 0.180 0.180
0.094 0.145 0.165
Tip Radius R2 in.
9.69 9.69
7.88 8.56
6.75 6.38 6.38 6.25 6.25 6.25
4.88 4.88 4.38 4.38 4.38
1.13 2.38 3.38
d1 in.
Table 9 WIDE FLANGE BEAMS
11.8 15.6
9.71 6.21
5.02 7.08 9.12 9.55 10.1 11.1
3.54 4.59 6.68 7.06 7.81
1.22 4.05 5.52
Area A in2
310 426
171 107
56.7 84.2 110 113 116 121
21.8 30.2 44.3 45.4 47.6
0.782 10.8 23.9
Ix in.4
51.9 70.7
35.1 21.6
14.2 21.0 27.4 28.3 29.0 30.3
7.25 10.1 14.8 15.1 15.9
0.782 5.40 9.58
Sx in.3
Axis x-x
5.13 5.23
4.20 4.15
3.36 3.44 3.47 3.45 3.40 3.31
2.48 2.56 2.57 2.54 2.47
0.80 1.63 2.08
rx in.
44.1 96.1
36.5 10.8
7.44 18.2 37.0 33.9 34.7 36.5
2.98 9.69 14.0 14.5 15.5
0.275 3.52 7.73
Iy in.4
11.0 19.2
9.16 3.75
2.83 5.61 9.24 8.47 8.68 9.13
1.49 3.23 4.67 4.83 5.16
0.275 1.76 3.09
Sy in.3
Axis y-y
1.94 2.48
1.94 1.32
1.22 1.61 2.01 1.88 1.86 1.82
0.92 1.45 1.45 1.43 1.41
0.47 0.93 1.18
ry in.
V-14
January 2010
2.500 3.000 3.000 4.000 4.000 4.000 4.000 4.000 5.000
Designation
WF(A-N) 2 × 0.928 WF(A-N) 3 × 0.769 WF(A-N) 3 × 1.00 WF(A-N) 4 × 1.14 WF(A-N) 4 × 1.79 WF(A-N) 4 × 2.35 WF(A-N) 4 × 3.06 WF(A-N) 4 × 4.14 WF(A-N) 5 × 5.36
2.000 2.000 2.000 2.000 3.000 3.500 3.500 4.000 5.000
Width b in. 0.125 0.094 0.125 0.125 0.156 0.188 0.250 0.312 0.312
0.125 0.094 0.125 0.125 0.156 0.188 0.250 0.312 0.312
Web Thickness tw in. 0.156 0.156 0.156 0.125 0.188 0.188 0.188 0.250 0.312
Fillet Radius R1 in. 0.125 0.094 0.125 0.125 0.156 0.188 0.250 0.312 0.125
Tip Radius R2 in.
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
Flange Thickness tf in. 2.00 2.50 2.50 3.50 3.25 3.25 3.00 2.75 3.75
d1 in. 0.789 0.654 0.851 0.969 1.52 2.00 2.60 3.52 4.56
Area A in2 0.831 0.992 1.26 2.42 4.14 5.52 6.97 9.39 19.7
Ix in4
0.665 0.661 0.841 1.21 2.07 2.76 3.48 4.70 7.86
Sx in3
Axis x-x
1.03 1.23 1.22 1.58 1.65 1.66 1.64 1.63 2.08
rx in.
Table 10 WIDE FLANGE BEAMS–ARMY-NAVY SERIES
0.155 0.118 0.155 0.155 0.659 1.26 1.64 3.03 6.43
Iy in4
0.155 0.118 0.155 0.155 0.439 0.719 0.936 1.51 2.57
Sy in3
Axis y-y
0.443 0.426 0.426 0.400 0.658 0.793 0.793 0.927 1.19
ry in.
0.235 0.265 0.344 0.626 2.59 4.88 6.28 11.3 35.7
Cw in6
0.00407 0.00189 0.00439 0.00505 0.0123 0.0235 0.0547 0.115 0.146
J in4
1.12 1.30 1.29 1.63 1.78 1.84 1.82 1.88 2.39
r0 in.
January 2010
V-15
3.000 3.000
4.000 4.000
5.000 5.000 5.000
6.000 6.000 6.000
7.000
8.000 8.000 8.000
9.000
10.000 10.000 10.000
12.000 12.000 12.000 12.000 12.000
Designation
S 3 × 1.96 S 3 × 2.59
S 4 × 2.64 S 4 × 3.28
S 5 × 3.43 S 5 × 4.23 S 5 × 5.10
S 6 × 4.30 S 6 × 5.10 S 6 × 5.96
S 7 × 6.05
S 8 × 6.35 S 8 × 7.96 S 8 × 8.81
S 9 × 7.51
S 10 × 8.76 S 10 × 10.4 S 10 × 12.1
S 12 × 11.0 S 12 × 12.1 S 12 × 14.1 S 12 × 15.6 S 12 × 17.3
5.000 5.078 5.250 5.355 5.477
4.660 4.797 4.944
4.330
4.000 4.171 4.262
3.755
3.330 3.443 3.565
3.000 3.137 3.284
2.660 2.796
2.330 2.509
Width b in.
0.350 0.350 0.460 0.460 0.460
0.310 0.310 0.310
0.290
0.270 0.270 0.270
0.250
0.230 0.230 0.230
0.210 0.210 0.210
0.190 0.190
0.170 0.170
Flange Tip Thickness tf in.
0.544 0.544 0.660 0.660 0.660
0.491 0.491 0.491
0.458
0.425 0.425 0.425
0.392
0.359 0.359 0.359
0.326 0.326 0.326
0.293 0.293
0.260 0.260
Avg Flange Thickness t in.
0.350 0.428 0.460 0.565 0.687
0.310 0.447 0.594
0.290
0.270 0.441 0.532
0.345
0.230 0.343 0.465
0.210 0.347 0.494
0.190 0.326
0.170 0.349
Web Thickness tw in.
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
0.450 0.450 0.560 0.560 0.560
0.410 0.410 0.410
0.390
0.370 0.370 0.370
0.350
0.330 0.330 0.330
0.310 0.310 0.310
0.290 0.290
0.270 0.270
Fillet Radius R1 in.
0.210 0.210 0.280 0.280 0.280
0.190 0.190 0.190
0.170
0.160 0.160 0.160
0.150
0.140 0.140 0.140
0.130 0.130 0.130
0.110 0.110
0.100 0.100
Tip Radius R2 in.
9.75 9.75 9.25 9.25 9.25
8.00 8.00 8.00
7.00
6.25 6.25 6.25
5.25
4.50 4.50 4.50
3.50 3.50 3.50
2.75 2.75
1.75 1.75
d1 in.
Table 11 AMERICAN STANDARD I-BEAMS
9.35 10.3 12.0 13.2 14.7
7.45 8.82 10.3
6.38
5.40 6.77 7.49
5.15
3.66 4.34 5.07
2.92 3.60 4.34
2.25 2.79
1.67 2.21
Area A in2
218 229 272 287 305
123 135 147
85.9
57.6 64.9 68.7
39.4
22.1 24.1 26.3
12.3 13.7 15.2
6.06 6.79
2.52 2.93
Ix in4
36.4 38.2 45.4 47.9 50.8
24.5 27.0 29.4
19.1
14.4 16.2 17.2
11.3
7.36 8.04 8.77
4.90 5.48 6.09
3.03 3.39
1.68 1.95
Sx in3
Axis x-x
4.83 4.72 4.77 4.66 4.56
4.07 3.91 3.78
3.67
3.27 3.10 3.03
2.77
2.46 2.36 2.28
2.05 1.95 1.87
1.64 1.56
1.23 1.15
rx in.
9.35 9.87 13.5 14.5 15.7
6.78 7.50 8.36
5.09
3.73 4.31 4.66
2.88
1.82 2.04 2.31
1.21 1.41 1.66
0.76 0.90
0.46 0.59
Iy in4
3.74 3.89 5.16 5.42 5.74
2.91 3.13 3.38
2.35
1.86 2.07 2.19
1.53
1.09 1.19 1.30
0.81 0.90 1.01
0.57 0.65
0.39 0.47
Sy in3
Axis y-y
1.00 0.98 1.06 1.05 1.03
0.95 0.92 0.90
0.89
0.83 0.80 0.79
0.75
0.71 0.69 0.68
0.64 0.63 0.62
0.58 0.57
0.52 0.52
ry in.
V-16
January 2010
4.000
5.000
6.000 6.000 6.000
7.000
8.000 8.000
10.000 10.000
12.000 12.000
I 4 × 2.68
I 5 × 4.05
I 6 × 3.92 I 6 × 4.82 I 6 × 5.46
I 7 × 5.79
I 8 × 6.12 I 8 × 8.77
I 10 × 9.83 I 10 × 11.3
I 12 × 12.5 I 12 × 15.5
5.500 6.500
5.000 6.000
4.000 5.000
4.000
3.000 3.500 4.000
3.500
3.000
2.500
Width b in.
0.625 0.625
0.500 0.500
0.375 0.500
0.375
0.312 0.375 0.375
0.312
0.250
0.250
Flange Thickness tf in.
0.375 0.437
0.343 0.375
0.281 0.312
0.281
0.250 0.250 0.281
0.250
0.188
0.188
Web Thickness tw in.
0.625 0.625
0.562 0.562
0.437 0.562
0.438
0.375 0.438 0.437
0.437
0.375
0.375
Fillet Radius R in.
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
3.000
I 3 × 2.16
Designation
Depth d in.
10.6 13.2
8.36 9.65
5.20 7.46
4.92
3.34 4.10 4.64
3.44
2.28
1.84
Area A in2
252 317
139 163
54.6 82.4
40.2
19.2 24.9 28.2
14.5
6.28
2.78
Ix in4
42.0 52.9
27.8 32.7
13.6 20.6
11.5
6.40 8.28 9.40
5.79
3.14
1.85
Sx in3
Axis x-x
Table 12 CANADIAN I-BEAMS
4.88 4.91
4.08 4.12
3.24 3.32
2.86
2.40 2.46 2.47
2.05
1.66
1.23
rx in.
15.7 28.7
10.5 18.1
4.02 10.5
4.02
1.42 2.70 4.02
2.24
1.13
0.657
Iy in4
5.70 8.84
4.19 6.02
2.01 4.18
2.01
0.945 1.54 2.01
1.28
0.754
0.525
Sy in3
Axis y-y
1.22 1.48
1.12 1.37
0.880 1.18
0.904
0.652 0.811 0.931
0.808
0.705
0.597
ry in.
513 929
236 408
58.5 147
44.1
11.5 21.3 31.8
12.3
3.98
1.24
Cw in6
0.193 0.245
0.127 0.140
0.048 0.116
0.048
0.026 0.043 0.048
0.036
0.017
0.017
J in4
5.03 5.13
4.23 4.34
3.36 3.53
3.00
2.49 2.59 2.64
2.20
1.80
1.37
r0 in.
January 2010
V-17
4.000
6.000 6.000
8.000
Designation
WF 4 × 4.12
WF 6 × 7.61 WF 6 × 9.66
WF 8 × 13.1
8.000
6.000 6.000
4.000
Width b in.
0.500
0.375 0.500
0.312
Flange Thickness tf in.
0.375
0.312 0.375
0.250
Web Thickness tw in.
0.750
0.625 0.625
0.437
Fillet Radius R in.
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
11.1
6.47 8.21
3.50
Area A in2
129
41.5 51.2
9.72
Ix in4
32.2
13.8 17.1
4.86
Sx in3
Axis x-x
3.40
2.53 2.50
1.67
rx in.
Table 13 CANADIAN WIDE FLANGE BEAMS
42.8
13.5 18.1
3.34
Iy in4
10.7
4.52 6.02
1.67
Sy in3
Axis y-y
1.96
1.45 1.48
0.977
ry in.
601
107 137
11.4
Cw in6
0.267
0.117 0.176
0.036
J in4
3.93
2.91 2.91
1.93
r0 in.
V-18
January 2010
Depth d in. 1.500 1.500 1.750 1.750 1.750 2.000 2.000 2.000 2.000 2.000 2.500 2.500 2.500 2.500 2.500 2.500 3.000 3.000 3.000 3.000 3.000 3.500 3.500 3.500 3.500
Designation
L 1 1/2 × 1 1/2 × 1/8 L 1 1/2 × 1 1/2 × 1/4
L 1 3/4 × 1 3/4 × 1/8 L 1 3/4 × 1 3/4 × 1/4 L 1 3/4 × 1 3/4 × 3/8
L 2 × 2 × 1/8 L 2 × 2 × 3/16 L 2 × 2 × 1/4 L 2 × 2 × 5/16 L 2 × 2 × 3/8
L 2 1/2 × 2 1/2 × 1/8 L 2 1/2 × 2 1/2 × 3/16 L 2 1/2 × 2 1/2 × 1/4 L 2 1/2 × 2 1/2 × 5/16 L 2 1/2 × 2 1/2 × 3/8 L 2 1/2 × 2 1/2 × 1/2
L 3 × 3 × 3/16 L 3 × 3 × 1/4 L 3 × 3 × 5/16 L 3 × 3 × 3/8 L 3 × 3 × 1/2
L 3 1/2 × 3 1/2 × 1/4 L 3 1/2 × 3 1/2 × 5/16 L 3 1/2 × 3 1/2 × 3/8 L 3 1/2 × 3 1/2 × 1/2
3.500 3.500 3.500 3.500
3.000 3.000 3.000 3.000 3.000
2.500 2.500 2.500 2.500 2.500 2.500
2.000 2.000 2.000 2.000 2.000
1.750 1.750 1.750
1.500 1.500
Width b in.
0.250 0.313 0.375 0.500
0.188 0.250 0.312 0.375 0.500
0.125 0.188 0.250 0.312 0.375 0.500
0.125 0.188 0.250 0.312 0.375
0.125 0.250 0.375
0.125 0.250
Thickness t in.
0.375 0.375 0.375 0.375
0.312 0.312 0.312 0.312 0.312
0.250 0.250 0.250 0.250 0.250 0.250
0.250 0.250 0.250 0.250 0.250
0.188 0.188 0.188
0.188 0.188
Fillet Radius R1 in.
0.250 0.250 0.250 0.250
0.250 0.250 0.250 0.250 0.250
0.125 0.125 0.125 0.125 0.125 0.125
0.125 0.125 0.125 0.125 0.125
0.125 0.125 0.125
0.125 0.125
Tip Radius R2 in.
1.99 2.47 2.93 3.83
1.28 1.68 2.08 2.47 3.23
0.72 1.07 1.40 1.73 2.05 2.65
0.58 0.85 1.11 1.36 1.61
0.50 0.96 1.38
0.42 0.81
Weight lb/ft
Table 14 ANGLES – EQUAL LEGS
1.69 2.10 2.49 3.25
1.09 1.43 1.77 2.10 2.74
0.616 0.911 1.19 1.47 1.74 2.26
0.491 0.723 0.944 1.16 1.37
0.423 0.813 1.17
0.360 0.688
Area A in2
1.94 2.38 2.79 3.57
0.908 1.19 1.45 1.71 2.17
0.369 0.539 0.695 0.839 0.976 1.22
0.185 0.268 0.342 0.410 0.474
0.121 0.223 0.306
0.0745 0.135
Ix , Iy in4
0.758 0.942 1.12 1.45
0.412 0.547 0.677 0.804 1.04
0.200 0.297 0.388 0.475 0.560 0.718
0.126 0.186 0.242 0.295 0.346
0.0948 0.182 0.259
0.0684 0.130
Sx , Sy in3
1.07 1.07 1.06 1.05
0.914 0.912 0.907 0.901 0.889
0.774 0.769 0.763 0.756 0.749 0.735
0.613 0.608 0.602 0.595 0.589
0.535 0.523 0.511
0.455 0.444
rx , ry in.
Axis x-x, y-y
0.947 0.974 1.00 1.05
0.797 0.826 0.852 0.877 0.924
0.655 0.684 0.710 0.734 0.757 0.802
0.531 0.560 0.585 0.609 0.632
0.473 0.524 0.570
0.411 0.461
x, y in.
0.739 0.924 1.10 1.45
0.332 0.450 0.563 0.674 0.888
0.143 0.213 0.278 0.341 0.403 0.525
0.071 0.106 0.138 0.169 0.201
0.0462 0.0904 0.132
0.0282 0.0556
Iz in4
rz in.
0.661 0.664 0.665 0.667
0.553 0.560 0.564 0.566 0.569
0.483 0.484 0.483 0.482 0.481 0.482
0.381 0.382 0.382 0.383 0.383
0.330 0.333 0.336
0.280 0.284
Axis z-z
January 2010
V-19
4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 5.000 5.000 5.000 5.000 5.000 5.000 6.000 6.000 6.000 6.000 6.000 8.000 8.000 8.000 8.000
Designation
L 4 × 4 × 1/4 L 4 × 4 × 5/16 L 4 × 4 × 3/8 L 4 × 4 × 7/16 L 4 × 4 × 1/2 L 4 × 4 × 9/16 L 4 × 4 × 5/8 L 4 × 4 × 11/16 L 4 × 4 × 3/4
L 5 × 5 × 3/8 L 5 × 5 × 7/16 L 5 × 5 × 1/2 L 5 × 5 × 9/16 L 5 × 5 × 5/8 L 5 × 5 × 3/4
L 6 × 6 × 3/8 L 6 × 6 × 7/16 L 6 × 6 × 1/2 L 6 × 6 × 5/8 L 6 × 6 × 3/4
L 8 × 8 × 1/2 L 8 × 8 × 5/8 L 8 × 8 × 3/4 L8×8×1
8.000 8.000 8.000 8.000
6.000 6.000 6.000 6.000 6.000
5.000 5.000 5.000 5.000 5.000 5.000
4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000
Width b in.
0.500 0.625 0.750 1.000
0.375 0.438 0.500 0.625 0.750
0.375 0.438 0.500 0.563 0.625 0.750
0.250 0.313 0.375 0.438 0.500 0.563 0.625 0.688 0.750
Thickness t in.
0.625 0.625 0.625 0.625
0.500 0.500 0.500 0.500 0.500
0.500 0.500 0.500 0.500 0.500 0.500
0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375
Fillet Radius R1 in.
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
0.375 0.375 0.375 0.375
0.375 0.375 0.375 0.375 0.375
0.375 0.375 0.375 0.375 0.375 0.375
0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250
Tip Radius R2 in.
9.14 11.3 13.5 17.7
5.12 5.95 6.75 8.35 9.91
4.24 4.92 5.58 6.24 6.88 8.15
2.28 2.83 3.37 3.90 4.41 4.93 5.42 5.92 6.40
Weight lb/ft
7.77 9.63 11.5 15.0
4.35 5.06 5.74 7.10 8.43
3.60 4.18 4.74 5.31 5.85 6.93
1.94 2.41 2.86 3.32 3.75 4.19 4.61 5.03 5.44
Area A in2
47.8 58.6 68.9 88.2
14.9 17.2 19.4 23.7 27.7
8.40 9.69 10.9 12.1 13.3 15.4
2.94 3.62 4.26 4.89 5.47 6.04 6.57 7.09 7.58
Ix , Iy in4
8.18 10.1 12.0 15.6
3.39 3.94 4.48 5.52 6.53
2.31 2.68 3.04 3.40 3.75 4.42
1.00 1.25 1.48 1.71 1.93 2.15 2.36 2.57 2.77
Sx , Sy in3
2.48 2.47 2.45 2.42
1.85 1.84 1.84 1.83 1.81
1.53 1.52 1.52 1.51 1.50 1.49
1.23 1.23 1.22 1.21 1.21 1.20 1.19 1.19 1.18
rx , ry in.
Axis x-x, y-y
2.16 2.21 2.26 2.35
1.61 1.64 1.66 1.71 1.76
1.36 1.39 1.41 1.44 1.46 1.51
1.07 1.10 1.12 1.15 1.17 1.20 1.22 1.24 1.27
x, y in.
18.8 23.2 27.5 35.9
5.69 6.65 7.58 9.39 11.1
3.19 3.73 4.25 4.77 5.28 6.27
1.13 1.41 1.68 1.95 2.20 2.46 2.71 2.96 3.21
Iz in4
rz in.
1.55 1.55 1.55 1.55
1.14 1.15 1.15 1.15 1.15
0.941 0.945 0.947 0.948 0.949 0.951
0.762 0.765 0.766 0.766 0.766 0.766 0.766 0.767 0.768
Axis z-z
Table 15 SQUARE END ANGLES – EQUAL LEGS Depth d in.
Width b in.
Thickness t in.
Area A in2
Axis x-x, y-y
Axis z-z
Designation LS 1 × 1 × 1/8 LS 1 × 1 × 3/16 LS 1 × 1 × 1/4
1.000 1.000 1.000
1.000 1.000 1.000
0.125 0.188 0.250
Weight lb/ft 0.28 0.40 0.51
0.234 0.341 0.438
Ix , Iy in4 0.0217 0.0300 0.0369
Sx , Sy in3 0.0309 0.0440 0.0558
rx , ry in. 0.304 0.297 0.290
x, y in. 0.296 0.318 0.339
Iz in4 0.00896 0.0129 0.0168
rz in. 0.196 0.195 0.196
LS 1 1/4 × 1 1/4 × 1/8 LS 1 1/4 × 1 1/4 × 3/16 LS 1 1/4 × 1 1/4 × 1/4
1.250 1.250 1.250
1.250 1.250 1.250
0.125 0.188 0.250
0.35 0.51 0.66
0.297 0.435 0.563
0.0439 0.0616 0.0767
0.0493 0.0709 0.0905
0.385 0.377 0.369
0.359 0.381 0.403
0.0179 0.0258 0.0333
0.246 0.244 0.243
LS 1 1/2 × 1 1/2 × 1/8 LS 1 1/2 × 1 1/2 × 3/16 LS 1 1/2 × 1 1/2 × 1/4
1.500 1.500 1.500
1.500 1.500 1.500
0.125 0.188 0.250
0.42 0.62 0.81
0.359 0.529 0.688
0.0778 0.110 0.139
0.0721 0.104 0.134
0.465 0.457 0.449
0.421 0.444 0.466
0.0315 0.0455 0.0586
0.296 0.293 0.292
LS 1 3/4 × 1 3/4 × 1/8 LS 1 3/4 × 1 3/4 × 3/16 LS 1 3/4 × 1 3/4 × 1/4
1.750 1.750 1.750
1.750 1.750 1.750
0.125 0.188 0.250
0.50 0.73 0.96
0.422 0.623 0.813
0.126 0.179 0.227
0.099 0.144 0.186
0.546 0.537 0.529
0.484 0.507 0.529
0.0507 0.0734 0.0947
0.347 0.343 0.341
LS 2 × 2 × 1/8 LS 2 × 2 × 3/16 LS 2 × 2 × 1/4
2.000 2.000 2.000
2.000 2.000 2.000
0.125 0.188 0.250
0.57 0.84 1.10
0.484 0.717 0.938
0.190 0.273 0.348
0.131 0.191 0.247
0.626 0.617 0.609
0.546 0.569 0.592
0.0766 0.111 0.143
0.398 0.394 0.391
LS 2 1/2 × 2 1/2 × 1/8 LS 2 1/2 × 2 1/2 × 3/16 LS 2 1/2 × 2 1/2 × 1/4 LS 2 1/2 × 2 1/2 × 5/16
2.500 2.500 2.500 2.500
2.500 2.500 2.500 2.500
0.125 0.188 0.250 0.312
0.72 1.06 1.40 1.72
0.609 0.905 1.19 1.46
0.378 0.548 0.703 0.847
0.207 0.303 0.394 0.481
0.787 0.778 0.769 0.761
0.671 0.695 0.717 0.739
0.152 0.222 0.287 0.350
0.499 0.495 0.491 0.489
LS 3 × 3 × 1/8 LS 3 × 3 × 3/16 LS 3 × 3 × 1/4 LS 3 × 3 × 5/16
3.000 3.000 3.000 3.000
3.000 3.000 3.000 3.000
0.125 0.188 0.250 0.312
0.86 1.28 1.69 2.09
0.734 1.09 1.44 1.77
0.661 0.964 1.24 1.51
0.300 0.442 0.577 0.706
0.949 0.939 0.930 0.922
0.797 0.820 0.842 0.865
0.265 0.388 0.504 0.616
0.601 0.596 0.592 0.589
LS 3 1/2 × 3 1/2 × 1/8
3.500
3.500
0.125
1.01
0.859
1.06
0.411
1.11
0.922
0.425
0.703
LS 4 × 4 × 1/8 LS 4 × 4 × 1/4
4.000 4.000
4.000 4.000
0.125 0.250
1.16 2.28
0.984 1.94
1.59 3.04
0.539 1.05
1.27 1.25
1.05 1.09
0.638 1.22
0.805 0.795
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
V-20
January 2010
January 2010
V-21
Depth d in.
1.750 1.750 1.750
2.000
2.000 2.000
2.000 2.000 2.000 2.000
2.000
2.250
2.500
2.500 2.500 2.500 2.500 2.500
2.500 2.500 2.500 2.500 2.500
3.000
3.000 3.000 3.000 3.000 3.000
Designation
L 1 3/4 × 1 1/4 × 1/8 L 1 3/4 × 1 1/4 × 3/16 L 1 3/4 × 1 1/4 × 1/4
L 2 × 1 × 3/16
L 2 × 1 1/4 × 1/8 L 2 × 1 1/4 × 1/4
L 2 × 1 1/2 × 1/8 L 2 × 1 1/2 × 3/16 L 2 × 1 1/2 × 1/4 L 2 × 1 1/2 × 3/8
L 2 × 1 3/4 × 1/4
L 2 1/4 × 1 1/2 × 1/4
L 2 1/2 × 1 1/4 × 1/8
L 2 1/2 × 1 1/2 × 1/8 L 2 1/2 × 1 1/2 × 3/16 L 2 1/2 × 1 1/2 × 1/4 L 2 1/2 × 1 1/2 × 5/16 L 2 1/2 × 1 1/2 × 3/8
L 2 1/2 × 2 × 1/8 L 2 1/2 × 2 × 3/16 L 2 1/2 × 2 × 1/4 L 2 1/2 × 2 × 5/16 L 2 1/2 × 2 × 3/8
L 3 × 1 1/2 × 1/4
L 3 × 2 × 3/16 L 3 × 2 × 1/4 L 3 × 2 × 5/16 L 3 × 2 × 3/8 L 3 × 2 × 1/2
2.000 2.000 2.000 2.000 2.000
1.500
2.000 2.000 2.000 2.000 2.000
1.500 1.500 1.500 1.500 1.500
1.250
1.500
1.750
1.500 1.500 1.500 1.500
1.250 1.250
1.000
1.250 1.250 1.250
Width b in.
0.188 0.250 0.312 0.375 0.500
0.250
0.125 0.188 0.250 0.312 0.375
0.125 0.188 0.250 0.312 0.375
0.125
0.250
0.250
0.125 0.188 0.250 0.375
0.125 0.250
0.188
0.125 0.188 0.250
Thickness t in.
0.312 0.312 0.312 0.312 0.312
0.312
0.250 0.250 0.250 0.250 0.250
0.250 0.250 0.250 0.250 0.250
0.188
0.250
0.250
0.188 0.188 0.188 0.188
0.188 0.188
0.188
0.188 0.188 0.188
Fillet Radius R1 in.
0.188 0.188 0.188 0.188 0.188
0.125
0.125 0.125 0.125 0.125 0.125
0.125 0.125 0.125 0.125 0.125
0.094
0.125
0.125
0.125 0.125 0.125 0.125
0.125 0.125
0.125
0.125 0.125 0.125
Tip Radius R2 in.
1.07 1.40 1.73 2.05 2.65
1.27
0.65 0.96 1.26 1.54 1.83
0.58 0.85 1.11 1.36 1.61
0.54
1.04
1.04
0.50 0.73 0.96 1.38
0.46 0.88
0.62
0.42 0.62 0.81
Weight lb/ft
0.910 1.19 1.47 1.74 2.26
1.08
0.554 0.817 1.07 1.31 1.55
0.491 0.723 0.944 1.16 1.37
0.457
0.882
0.882
0.423 0.624 0.813 1.17
0.392 0.751
0.530
0.360 0.530 0.688
Area A in2
0.821 1.06 1.29 1.51 1.90
0.980
0.345 0.503 0.646 0.780 0.905
0.314 0.457 0.586 0.705 0.816
0.298
0.435
0.328
0.168 0.243 0.311 0.428
0.158 0.291
0.211
0.109 0.157 0.199
Ix in4
rx in.
0.400 0.526 0.647 0.765 0.987
0.510
0.194 0.288 0.375 0.459 0.541
0.186 0.275 0.358 0.437 0.514
0.182
0.292
0.237
0.120 0.178 0.231 0.330
0.117 0.224
0.166
0.949 0.944 0.938 0.931 0.918
0.954
0.789 0.784 0.778 0.770 0.763
0.800 0.794 0.787 0.780 0.773
0.807
0.702
0.610
0.630 0.625 0.618 0.604
0.635 0.623
0.631
0.0901 0.549 0.133 0.544 0.172 0.537
Sx in3
Axis x-x y in.
0.947 0.976 1.00 1.03 1.08
1.08
0.722 0.752 0.778 0.802 0.826
0.806 0.838 0.864 0.889 0.914
0.867
0.758
0.617
0.605 0.633 0.657 0.704
0.649 0.702
0.728
0.544 0.572 0.596
Table 16 ANGLES – UNEQUAL LEGS
0.292 0.377 0.456 0.529 0.659
0.165
0.197 0.286 0.366 0.440 0.509
0.0860 0.124 0.158 0.188 0.216
0.0515
0.153
0.233
0.0810 0.117 0.148 0.202
0.0477 0.0862
0.0351
0.0460 0.0659 0.0830
Iy in4
0.190 0.249 0.306 0.361 0.464
0.142
0.129 0.191 0.249 0.304 0.358
0.0728 0.108 0.140 0.170 0.200
0.0516
0.138
0.185
0.0710 0.105 0.136 0.193
0.0492 0.0937
0.0459
0.0484 0.0713 0.0921
Sy in3
ry in.
0.567 0.562 0.557 0.551 0.541
0.391
0.596 0.592 0.585 0.579 0.572
0.418 0.414 0.408 0.403 0.398
0.336
0.417
0.514
0.438 0.433 0.427 0.415
0.349 0.339
0.257
0.357 0.353 0.347
Axis y-y
0.459 0.485 0.510 0.534 0.580
0.343
0.478 0.506 0.531 0.555 0.578
0.320 0.347 0.372 0.395 0.419
0.252
0.389
0.494
0.360 0.386 0.410 0.455
0.281 0.330
0.236
0.300 0.326 0.349
x in.
0.158 0.209 0.257 0.305 0.399
0.106
0.0955 0.142 0.185 0.226 0.267
0.0492 0.0727 0.0946 0.116 0.137
0.0320
0.0877
0.109
0.0407 0.0606 0.0792 0.116
0.0265 0.0515
0.0223
0.0238 0.0355 0.0465
Iz in4
0.416 0.418 0.419 0.419 0.421
0.313
0.415 0.416 0.416 0.415 0.415
0.316 0.317 0.316 0.316 0.316
0.265
0.315
0.352
0.310 0.312 0.312 0.314
0.260 0.262
0.205
0.257 0.259 0.260
rz in.
Axis z-z
24.25 23.95 23.64 23.32 22.61
14.59
32.51 32.30 32.09 31.85 31.59
20.43 20.07 19.70 19.29 18.84
15.16
23.46
36.91
29.38 29.00 28.62 27.74
21.87 20.83
14.62
27.12 26.61 26.09
α (deg)
V-22
January 2010
Depth d in.
3.000 3.000 3.000
3.500 3.500 3.500 3.500
4.000 4.000 4.000 4.000 4.000 4.000
4.000 4.000 4.000
5.000 5.000 5.000 5.000
Designation
L 3 × 2 1/2 × 1/4 L 3 × 2 1/2 × 5/16 L 3 × 2 1/2 × 3/8
L 3 1/2 × 3 × 1/4 L 3 1/2 × 3 × 5/16 L 3 1/2 × 3 × 3/8 L 3 1/2 × 3 × 1/2
L 4 × 3 × 1/4 L 4 × 3 × 5/16 L 4 × 3 × 3/8 L 4 × 3 × 7/16 L 4 × 3 × 1/2 L 4 × 3 × 5/8
L 4 × 3 1/2 × 5/16 L 4 × 3 1/2 × 3/8 L 4 × 3 1/2 × 1/2
L 5 × 3 × 1/4 L 5 × 3 × 5/16 L 5 × 3 × 3/8 L 5 × 3 × 1/2
3.000 3.000 3.000 3.000
3.500 3.500 3.500
3.000 3.000 3.000 3.000 3.000 3.000
3.000 3.000 3.000 3.000
2.500 2.500 2.500
Width b in.
0.250 0.312 0.375 0.500
0.312 0.375 0.500
0.250 0.312 0.375 0.438 0.500 0.625
0.250 0.312 0.375 0.500
0.250 0.312 0.375
Thickness t in.
0.375 0.375 0.375 0.375
0.375 0.375 0.375
0.375 0.375 0.375 0.375 0.375 0.375
0.375 0.375 0.375 0.375
0.312 0.312 0.312
Fillet Radius R1 in.
0.312 0.312 0.312 0.312
0.312 0.312 0.312
0.250 0.250 0.250 0.250 0.250 0.250
0.250 0.250 0.250 0.250
0.250 0.250 0.250
Tip Radius R2 in.
2.26 2.81 3.35 4.40
2.62 3.13 4.10
1.99 2.46 2.93 3.38 3.83 4.69
1.84 2.27 2.71 3.53
1.54 1.90 2.25
Weight lb/ft
1.93 2.39 2.85 3.74
2.23 2.66 3.49
1.69 2.09 2.49 2.88 3.25 3.99
1.57 1.93 2.30 3.00
1.31 1.61 1.92
Area A in2
4.90 6.05 7.17 9.26
3.41 4.03 5.18
2.69 3.29 3.88 4.44 4.97 5.96
1.85 2.26 2.66 3.39
1.12 1.37 1.61
Ix in4
1.45 1.81 2.16 2.83
1.20 1.43 1.88
0.963 1.19 1.42 1.64 1.85 2.26
0.742 0.918 1.09 1.42
0.532 0.659 0.782
Sx in3
1.60 1.59 1.59 1.57
1.24 1.23 1.22
1.26 1.26 1.25 1.24 1.24 1.22
1.09 1.08 1.08 1.06
0.927 0.922 0.916
rx in.
Axis x-x
1.62 1.65 1.68 1.73
1.16 1.19 1.24
1.21 1.24 1.27 1.29 1.31 1.36
1.01 1.04 1.07 1.11
0.893 0.919 0.944
y in.
Iy in4
1.34 1.65 1.95 2.49
2.43 2.87 3.68
1.30 1.59 1.86 2.13 2.37 2.82
1.25 1.53 1.79 2.28
0.704 0.859 1.01
Table 16 ANGLES – UNEQUAL LEGS (Continued)
0.567 0.706 0.843 1.10
0.938 1.12 1.46
0.568 0.703 0.836 0.964 1.09 1.32
0.559 0.692 0.822 1.07
0.380 0.470 0.557
Sy in3
ry in.
0.834 0.831 0.827 0.816
1.04 1.04 1.03
0.875 0.871 0.865 0.859 0.853 0.841
0.893 0.888 0.883 0.871
0.734 0.730 0.724
Axis y-y
0.639 0.666 0.692 0.742
0.913 0.940 0.989
0.719 0.746 0.771 0.796 0.819 0.866
0.767 0.793 0.819 0.867
0.647 0.672 0.697
x in.
0.739 0.930 1.12 1.47
1.06 1.28 1.70
0.651 0.810 0.967 1.12 1.27 1.56
0.562 0.701 0.838 1.10
0.323 0.404 0.484
Iz in4
0.620 0.624 0.626 0.628
0.691 0.694 0.698
0.620 0.623 0.624 0.624 0.624 0.625
0.599 0.602 0.603 0.605
0.497 0.500 0.503
rz in.
Axis z-z
20.79 20.54 20.31 19.86
37.33 37.22 37.00
29.39 29.19 29.00 28.81 28.62 28.20
36.17 36.04 35.90 35.63
34.65 34.45 34.25
α (deg)
January 2010
V-23
5.000 5.000 5.000 5.000
6.000
6.000 6.000 6.000 6.000
6.000 6.000 6.000 6.000 6.000
7.000
8.000 8.000 8.000
Designation
L 5 × 3 1/2 × 5/16 L 5 × 3 1/2 × 3/8 L 5 × 3 1/2 × 1/2 L 5 × 3 1/2 × 5/8
L 6 × 3 x 3/8
L 6 × 3 1/2 × 5/16 L 6 × 3 1/2 × 3/8 L 6 × 3 1/2 × 1/2 L 6 × 3 1/2 × 5/8
L 6 × 4 × 3/8 L 6 × 4 × 7/16 L 6 × 4 × 1/2 L 6 × 4 × 5/8 L 6 × 4 × 3/4
L 7 × 4 × 1/2
L 8 × 6 × 5/8 L 8 × 6 × 11/16 L 8 × 6 × 3/4
6.000 6.000 6.000
4.000
4.000 4.000 4.000 4.000 4.000
3.500 3.500 3.500 3.500
3.000
3.500 3.500 3.500 3.500
Width b in.
0.625 0.688 0.750
0.500
0.375 0.438 0.500 0.625 0.750
0.312 0.375 0.500 0.625
0.375
0.312 0.375 0.500 0.625
Thickness t in.
0.500 0.500 0.500
0.500
0.500 0.500 0.500 0.500 0.500
0.500 0.500 0.500 0.500
0.500
0.438 0.438 0.438 0.438
Fillet Radius R1 in.
0.312 0.375 0.375
0.375
0.375 0.375 0.375 0.375 0.375
0.312 0.312 0.312 0.312
0.375
0.312 0.312 0.312 0.312
Tip Radius R2 in.
9.84 10.8 11.7
6.17
4.24 4.92 5.58 6.88 8.15
3.39 4.04 5.31 6.54
3.80
3.00 3.58 4.70 5.79
Weight lb/ft
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
8.37 9.15 9.93
5.24
3.60 4.18 4.74 5.85 6.93
2.88 3.43 4.51 5.56
3.23
2.55 3.05 4.00 4.92
Area A in2
53.6 58.1 62.6
26.1
13.0 15.1 17.0 20.7 24.1
10.6 12.6 16.4 19.8
11.8
6.39 7.58 9.79 11.8
Ix in4
9.74 10.6 11.5
5.66
3.19 3.70 4.20 5.18 6.12
2.64 3.16 4.15 5.10
3.03
1.86 2.22 2.91 3.57
Sx in3
2.53 2.52 2.51
2.23
1.90 1.90 1.89 1.88 1.87
1.92 1.92 1.90 1.89
1.91
1.58 1.58 1.56 1.55
rx in.
Axis x-x
2.50 2.52 2.55
2.39
1.91 1.93 1.96 2.01 2.06
1.97 2.00 2.06 2.11
2.11
1.56 1.59 1.64 1.69
y in.
26.0 28.`0 30.2
6.28
4.66 5.37 6.03 7.30 8.46
2.71 3.21 4.12 4.96
1.99
2.59 3.06 3.93 4.72
Iy in4
5.78 6.27 6.79
2.03
1.51 1.76 1.99 2.45 2.89
0.985 1.18 1.54 1.89
0.842
0.965 1.15 1.51 1.84
Sy in3
ry in.
1.76 1.75 1.74
1.09
1.14 1.13 1.13 1.12 1.10
0.971 0.967 0.956 0.944
0.786
1.01 1.00 0.991 0.979
Axis y-y
1.51 1.53 1.55
0.903
0.920 0.947 0.972 1.02 1.07
0.746 0.773 0.823 0.872
0.630
0.819 0.846 0.895 0.943
x in.
13.6 14.7 15.9
3.71
2.50 2.92 3.33 4.12 4.88
1.56 1.87 2.46 3.02
1.21
1.35 1.63 2.14 2.64
Iz in4
1.275 1.266 1.265
0.842
0.834 0.836 0.838 0.839 0.839
0.736 0.738 0.738 0.737
0.612
0.728 0.731 0.732 0.733
rz in.
Axis z-z
29.07 29.03 28.94
18.70
24.33 24.16 24.00 23.68 23.35
19.61 19.43 19.10 18.75
15.24
26.32 26.13 25.78 25.41
α (deg)
V-24
January 2010
1.000
1.250
1.500 1.500 1.500 1.500
1.750
2.000 2.000 2.000 2.000
2.500 2.500 2.500 2.500
3.000 3.000 3.000 3.000 3.000
3.500
4.000 4.000 4.000
5.000 5.000 5.000
5.250
Designation
LS 1 × 3/4 × 1/8
LS 1 1/4 × 1 × 1/8
LS 1 1/2 × 3/4 × 1/8 LS 1 1/2 × 1 × 1/8 LS 1 1/2 × 1 × 3/16 LS 1 1/2 × 1 1/4 × 1/8
LS 1 3/4 × 1 × 1/8
LS 2 × 1 × 1/8 LS 2 × 1 × 3/16 LS 2 × 1 1/2 × 1/8 LS 2 × 1 1/2 × 3/16
LS 2 1/2 × 1 × 1/8 LS 2 1/2 × 1 1/2 × 1/8 LS 2 1/2 × 2 × 1/8 LS 2 1/2 × 2 × 3/16
LS 3 × 1 × 1/8 LS 3 × 2 × 1/8 LS 3 × 2 × 1/4 LS 3 × 2 × 3/8 LS 3 × 2 1/2 × 1/4
LS 3 1/2 × 1 1/4 × 1/8
LS 4 × 2 × 1/8 LS 4 × 2 × 1/4 LS 4 × 3 × 1/8
LS 5 × 3 × 1/8 LS 5 × 3 × 1/4 LS 5 × 4 × 1/8
LS 5 ¼ × 2 ¼ × 1/8
2.250
3.000 3.000 4.000
2.000 2.000 3.000
1.250
1.000 2.000 2.000 2.000 2.500
1.000 1.500 2.000 2.000
1.000 1.000 1.500 1.500
1.000
0.750 1.000 1.000 1.250
1.000
0.750
Width b in.
0.125
0.125 0.250 0.125
0.125 0.250 0.125
0.125
0.125 0.125 0.250 0.375 0.250
0.125 0.125 0.125 0.188
0.125 0.188 0.125 0.188
0.125
0.125 0.125 0.188 0.125
0.125
0.125
Thickness t in.
1.08
1.16 2.28 1.30
0.86 1.69 1.01
0.68
0.57 0.72 1.40 2.04 1.54
0.50 0.57 0.64 0.95
0.42 0.62 0.50 0.73
0.39
0.31 0.35 0.51 0.39
0.31
0.24
Weight lb/ft
0.922
0.984 1.94 1.11
0.734 1.44 0.859
0.578
0.484 0.609 1.19 1.73 1.31
0.422 0.484 0.547 0.811
0.359 0.529 0.422 0.623
0.328
0.266 0.297 0.435 0.328
0.266
0.203
Area A in2
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
2.75
2.66 5.11 2.92
1.27 2.41 1.45
0.750
0.456 0.580 1.09 1.53 1.17
0.277 0.319 0.352 0.510
0.150 0.215 0.173 0.248
0.104
0.0613 0.0679 0.0959 0.0733
0.0408
0.0197
Ix in4
0.817
0.784 1.53 0.820
0.484 0.936 0.517
0.347
0.250 0.282 0.542 0.781 0.561
0.178 0.191 0.200 0.294
0.117 0.170 0.125 0.183
0.0909
0.0644 0.0677 0.0979 0.0702
0.0477
0.0295
Sx in3
rx in.
1.73
1.64 1.62 1.62
1.31 1.29 1.30
1.14
0.971 0.975 0.957 0.940 0.945
0.811 0.812 0.802 0.793
0.647 0.638 0.641 0.632
0.563
0.480 0.478 0.470 0.473
0.392
0.312
Axis x-x
1.89
1.61 1.66 1.44
1.38 1.43 1.19
1.34
1.18 0.947 0.993 1.04 0.911
0.942 0.829 0.741 0.764
0.715 0.738 0.618 0.641
0.604
0.548 0.497 0.520 0.455
0.393
0.332
y in.
0.340
0.762 1.44 1.70
0.229 0.421 0.719
0.0570
0.0286 0.213 0.392 0.543 0.743
0.0276 0.0899 0.203 0.292
0.0263 0.0366 0.0847 0.120
0.0255
0.0105 0.0245 0.0340 0.0465
0.0233
0.00947
Iy in4
Table 17 SQUARE END ANGLES – UNEQUAL LEGS
0.183
0.319 0.614 0.554
0.141 0.268 0.311
0.0550
0.0347 0.137 0.260 0.371 0.404
0.0342 0.0767 0.135 0.197
0.0335 0.0481 0.0748 0.108
0.0331
0.0183 0.0325 0.0465 0.0505
0.0318
0.0174
Sy in3
ry in.
0.607
0.880 0.861 1.24
0.558 0.541 0.914
0.314
0.243 0.592 0.574 0.559 0.753
0.256 0.431 0.609 0.600
0.271 0.263 0.448 0.439
0.279
0.199 0.287 0.280 0.376
0.296
0.216
Axis y-y
0.387
0.610 0.657 0.936
0.382 0.429 0.690
0.215
0.175 0.447 0.493 0.539 0.661
0.192 0.329 0.491 0.514
0.215 0.238 0.368 0.391
0.229
0.173 0.247 0.270 0.330
0.268
0.207
x in.
0.223
0.447 0.851 0.847
0.144 0.269 0.376
0.0392
0.0201 0.120 0.225 0.320 0.366
0.0187 0.0532 0.102 0.148
0.0168 0.0240 0.0447 0.0645
0.0156
0.00683 0.0140 0.0201 0.0228
0.0119
0.00519
Iz in4
0.491
0.674 0.663 0.874
0.442 0.432 0.661
0.261
0.204 0.444 0.435 0.430 0.528
0.210 0.331 0.432 0.427
0.216 0.213 0.326 0.322
0.218
0.160 0.217 0.215 0.264
0.212
0.160
rz in.
Axis z-z
12.17
20.67 20.36 32.63
15.40 14.95 29.45
8.98
7.94 24.28 23.77 23.18 34.37
10.54 20.36 32.46 32.26
14.95 14.45 29.16 28.84
18.50
14.62 23.77 23.18 34.37
32.05
28.49
α (deg)
Table 18 TEES Axis x-x Sx rx in3 in.
y in.
Iy in4
Axis y-y Sy in3
ry in.
0.293 0.363 0.359 0.433 0.438 0.606
0.292 0.326 0.352 0.437 0.464 0.624
0.011 0.038 0.056 0.056 0.075 0.060
0.023 0.051 0.075 0.075 0.100 0.080
0.206 0.319 0.328 0.312 0.319 0.286
0.26 0.31 0.33 0.09 0.50
0.59 0.58 0.66 0.31 0.74
0.58 0.61 0.64 0.30 0.73
0.18 0.23 0.26 0.285 0.44
0.18 0.23 0.23 0.22 0.35
0.41 0.42 0.46 0.57 0.52
1.49 0.94 1.83 0.60 1.72
0.72 0.51 0.86 0.40 0.77
0.91 0.72 0.89 0.51 0.86
0.92 0.68 0.88 0.48 0.75
0.44 0.75 0.90 2.10 1.77
0.35 0.50 0.60 1.05 0.89
0.50 0.65 0.63 0.96 0.87
3.18 3.59 4.60 2.52 3.42
4.56 8.56 10.8 1.78 2.37
1.58 2.43 3.14 0.78 1.06
1.20 1.54 1.54 0.84 0.83
1.11 1.48 1.54 0.71 0.76
2.12 2.13 2.83 2.52 4.13
1.06 1.06 1.42 1.12 1.65
0.82 0.77 0.79 1.00 1.10
0.094 0.062 0.187 0.062
0.13 0.16 0.54 0.32
0.013 0.018 0.11 0.043
0.017 0.021 0.10 0.045
0.31 0.34 0.45 0.37
0.25 0.26 0.44 0.30
0.007 0.017 0.054 0.049
0.013 0.023 0.072 0.056
0.24 0.33 0.32 0.39
0.094 0.187 0.250 0.312
0.157 0.187 0.250 0.312
0.47 0.64 0.96 1.51
0.45 0.12 0.35 0.86
0.22 0.11 0.25 0.49
0.98 0.44 0.60 0.76
0.92 0.39 0.59 0.74
0.063 0.13 0.17 0.42
0.063 0.13 0.17 0.33
0.37 0.45 0.42 0.53
0.375 0.312 0.375 0.375
0.375 0.312 0.375 0.375
0.375 0.312 0.375 0.375
2.17 1.98 2.92 2.92
1.78 0.93 4.40 2.06
0.84 0.49 1.54 0.90
0.91 0.69 1.23 0.84
0.89 0.60 1.14 0.72
0.86 1.68 2.03 3.93
0.58 0.84 1.01 1.57
0.63 0.92 0.83 1.16
0.625
0.500
0.625
8.92
3.17
2.95
4.44
1.27
Designation Td × b × Wt in. in. lb/ft
Thickness t in.
t1 in.
t2 in.
R1 in.
Area A in2
Ix in4
T 1.00 × 1.00 × 0.31 T 1.25 × 1.50 × 0.44 T 1.25 × 1.50 × 0.62 T 1.50 × 1.50 × 0.68 T 1.50 × 1.50 × 0.87 T 2.00 × 1.50 × 0.86
0.125 0.125 0.188 0.188 0.25 0.188
0.156 0.156 0.219 0.219 0.281 0.25
0.156 0.156 0.219 0.219 0.281 0.25
0.125 0.125 0.125 0.188 0.188 0.188
0.27 0.37 0.52 0.58 0.74 0.73
0.023 0.049 0.067 0.114 0.142 0.269
0.032 0.053 0.075 0.108 0.137 0.195
T 2.00 × 2.00 × 1.26 T 2.00 × 2.00 × 1.50 T 2.25 × 2.25 × 1.42 T 1.25 × 2.50 × 1.00 T 2.25 × 2.50 × 1.91
0.25 0.313 0.25 0.188 0.313
0.313 0.375 0.313 0.313 0.375
0.313 0.375 0.313 0.218 0.375
0.25 0.25 0.25 0.188 0.25
1.07 1.28 1.21 0.85 1.62
0.37 0.43 0.53 0.08 0.89
T 3.00 × 2.50 × 2.11 T 2.50 × 3.00 × 2.13 T 3.00 × 3.00 × 2.72 T 2.00 × 4.00 × 2.70 T 3.00 × 4.00 × 2.76
0.313 0.313 0.375 0.375 0.313
0.375 0.375 0.438 0.438 0.375
0.375 0.375 0.438 0.438 0.375
0.25 0.313 0.313 0.25 0.375
1.80 1.81 2.31 2.30 2.34
T 4.00 × 4.00 × 3.74 T 5.00 × 4.00 × 4.22 T 5.00 × 4.00 × 5.41 T 3.00 × 4.50 × 2.96 T 3.00 × 5.00 × 4.02
0.375 0.375 0.5 0.313 0.375
0.438 0.438 0.563 0.375 0.625
0.438 0.438 0.563 0.375 0.438
0.5 0.5 0.5 0.375 0.375
T 1.13 × 1.00 × 0.16 T 1.50 × 1.13 × 0.19 T 1.50 × 1.50 × 0.063 T 1.75 × 1.25 × 0.37
0.063 0.062 0.187 0.109
0.063 0.062 0.187 0.109
0.063 0.062 0.187 0.109
T 2.00 × 3.00 × 0.55 T 2.00 × 1.50 × 0.75 T 2.00 × 2.00 × 1.13 T 2.50 × 2.50 × 1.77
0.094 0.187 0.250 0.312
0.094 0.187 0.250 0.312
T 3.00 × 3.00 × 2.55 T 4.00 × 2.50 × 2.32 T 4.00 × 4.00 × 3.43 T 5.00 × 3.00 × 3.43
0.375 0.312 0.375 0.375
T 6.50 × 10.00 × 10.5(1)
0.500
89.7
12.7
14.4
1. t = 0.625 for flange and t = 0.500 for web 2. Users are encouraged to check availability with suppliers. 3. Tolerances for extruded shapes are given in Aluminum Standards and Data.
January 2010
V-25
Table 19 ARMY – NAVY AND SPECIAL TEES Designation T(A-N) d × b × Wt in. in. lb/ft
Stem Thickness ts in.
Flange Thickness tf in.
Area A in2
Axis x-x
Axis y-y
R1 in.
Ix in4
Sx in3
rx in.
y in.
Iy in4
Sy in3
ry in.
T(A-N) 1.25 × 1.50 × 0.384 T(A-N) 1.63 × 1.75 × 0.476 T(A-N) 1.00 × 2.00 × 0.421 T(A-N) 1.75 × 2.00 × 0.531 T(A-N) 1.25 × 2.50 × 0.652 T(A-N) 2.00 × 2.50 × 0.789
0.125 0.125 0.125 0.125 0.156 0.156
0.125 0.125 0.125 0.125 0.156 0.156
0.326 0.405 0.358 0.451 0.554 0.671
0.125 0.125 0.125 0.125 0.125 0.125
0.045 0.100 0.025 0.128 0.062 0.241
0.049 0.83 0.032 0.098 0.063 0.161
0.371 0.496 0.266 0.532 0.333 0.599
0.327 0.434 0.212 0.451 0.265 0.500
0.032 0.052 0.078 0.078 0.188 0.189
0.043 0.059 0.078 0.078 0.151 0.151
0.314 0.357 0.466 0.415 0.583 0.530
T(A-N) 2.00 × 3.00 × 0.881 T(A-N) 2.50 × 3.00 × 1.17 T(A-N) 3.00 × 4.00 × 1.50 T(A-N) 4.00 × 4.00 × 2.27 T(A-N) 5.00 × 4.00 × 2.57
0.156 0.188 0.188 0.250 0.250
0.156 0.188 0.188 0.250 0.250
0.749 0.995 1.28 1.93 2.18
0.125 0.188 0.188 0.250 0.250
0.254 0.565 1.03 2.98 5.54
0.164 0.302 0.448 1.02 1.57
0.582 0.753 0.897 1.24 1.59
0.456 0.632 0.708 1.08 1.47
0.330 0.393 0.947 1.24 1.24
0.220 0.262 0.474 0.619 0.620
0.663 0.629 0.861 0.801 0.754
T(A-N) 3.00 × 6.00 × 3.24 T(A-N) 4.00 × 6.00 × 3.88 T(A-N) 4.00 × 6.00 × 4.79 T(A-N) 7.50 × 7.50 × 9.46 T(A-N) 7.50 × 7.50 × 14.4 T(A-N) 6.00 × 8.00 × 11.2
0.3121 0.3751 0.3751 0. 5001 1.131 0.5001
0.312 0.313 0.450 0.750 0.750 0.860
2.75 3.30 4.07 8.04 12.3 9.56
0.3121 0.3131 0.3121 0.6251 0.6251 0.5001
1.83 4.78 5.02 40.3 69.3 22.9
0.77 1.59 1.61 7.28 14.5 4.82
0.81 1.20 1.11 2.24 2.38 1.55
0.62 1.00 0.88 1.96 2.71 1.24
5.63 5.65 8.12 13.6 14.4 36.8
1.88 1.88 2.71 4.53 4.80 9.19
1.43 1.31 1.41 1.30 1.08 1.96
1. Both Flange and stem of these shapes have square ends. Fillet radius R1 applies only to juncture of stem and flange. 2. Users are encouraged to check availability with suppliers. 3. Tolerances for extruded shapes are given in Aluminum Standards and Data.
V-26
January 2010
January 2010
V-27
1.750 2.000 2.375 3.000 3.000 4.000 4.062 4.125 4.000 4.125 5.000 5.062 5.000
Designation
Z 1 3/4 × 1 3/4 × 1.09
Z 2 × 1.25 × 0.922 Z 2 3/8 × 1 1/4 × 1.00
Z 3 × 2 11/16 × 2.33 Z 3 × 2 11/16 × 3.38
Z 4 × 3 1/16 × 2.85 Z 4 1/16 × 3 1/8 × 3.57 Z 4 1/8 × 3 3/16 × 4.32 Z 4 × 3 1/16 × 4.78 Z 4 1/8 × 3 3/16 × 6.22
Z 5 × 3 1/4 × 4.01 Z 5 1/16 × 3 5/16 × 4.84 Z 5 × 3 1/4 × 6.19
3.250 3.312 3.250
3.062 3.125 3.188 3.062 3.188
2.688 2.688
1.250 1.250
1.750
Width b in.
0.312 0.375 0.500
0.250 0.312 0.375 0.438 0.563
0.250 0.375
0.188 0.188
0.188
Thickness t in.
0.312 0.312 0.312
0.312 0.312 0.312 0.312 0.312
0.312 0.312
0.188 0.188
0.188
Fillet Radius R1 in.
1. Users are encouraged to check availability with suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Depth d in.
0.250 0.250 0.250
0.250 0.250 0.250 0.250 0.250
0.250 0.250
0.125 0.125
0.125
Tip Radius R2 in.
3.41 4.12 5.26
2.42 3.04 3.67 4.07 5.29
1.98 2.87
0.784 0.854
0.925
Area A in2 lx in4
13.4 16.2 19.2
6.31 7.96 9.66 9.69 12.8
2.89 3.86
0.459 0.695
0.447
Table 20 ZEES
5.36 6.41 7.69
3.16 3.92 4.69 4.84 6.19
1.92 2.57
0.459 0.586
0.511
Sx in3
Axis x-x
1.98 1.99 1.91
1.61 1.62 1.62 1.54 1.55
1.21 1.16
0.765 0.902
0.695
rx in.
5.93 7.40 8.82
4.01 5.23 6.54 6.53 9.06
2.64 3.76
0.186 0.187
0.553
ly in4
1.92 2.37 2.94
1.36 1.76 2.18 2.30 3.12
1.03 1.50
0.161 0.161
0.334
Sy in3
Axis y-y
1.32 1.34 1.29
1.29 1.31 1.33 1.27 1.31
1.15 1.14
0.488 0.467
0.773
ry in.
1.89 2.33 2.82
1.08 1.39 1.72 1.74 2.41
0.590 0.820
0.0630 0.0820
0.101
lz in4
0.745 0.752 0.732
0.668 0.676 0.684 0.654 0.675
0.545 0.534
0.284 0.310
0.330
rz in.
Axis z-z
30.67 31.13 31.15
36.78 37.40 37.92 37.83 38.68
43.40 44.52
29.20 23.20
48.82
α deg
Table 21 ROUND TUBES Inside Diameter in.
Weight lb/ft
Area A in2
I in4
S in3
r in.
J in4
Rb /t
WALL WALL WALL WALL WALL WALL WALL
1.376 1.312 1.250 1.188 1.124 1.000 0.750
0.329 0.488 0.635 0.775 0.911 1.15 1.56
0.280 0.415 0.540 0.659 0.775 0.982 1.33
0.0725 0.103 0.129 0.151 0.170 0.199 0.233
0.097 0.137 0.172 0.201 0.227 0.266 0.311
0.509 0.498 0.488 0.478 0.469 0.451 0.419
0.145 0.205 0.255 0.297 0.333 0.383 0.419
11.6 7.5 5.5 4.3 3.5 2.5 1.5
1.625 OD × 0.125 WALL 1.625 OD × 0.188 WALL 1.625 OD × 0.250 WALL
1.375 1.249 1.125
0.693 0.998 1.27
0.589 0.849 1.08
0.167 0.223 0.264
0.205 0.274 0.324
0.532 0.512 0.494
0.331 0.438 0.510
6.0 3.8 2.8
1.750 1.750 1.750 1.750
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.375
WALL WALL WALL WALL
1.500 1.374 1.250 1.000
0.750 1.08 1.39 1.90
0.638 0.923 1.18 1.62
0.212 0.285 0.341 0.411
0.242 0.326 0.389 0.470
0.576 0.556 0.538 0.504
0.421 0.563 0.663 0.766
6.5 4.2 3.0 1.8
1.875 1.875 1.875 1.875
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.375
WALL WALL WALL WALL
1.625 1.499 1.375 1.125
0.808 1.17 1.50 2.08
0.687 0.996 1.28 1.77
0.264 0.359 0.431 0.528
0.282 0.383 0.460 0.563
0.620 0.600 0.581 0.547
0.526 0.709 0.843 0.994
7.0 4.5 3.3 2.0
2.000 2.000 2.000 2.000 2.000 2.000
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500
WALL WALL WALL WALL WALL WALL
1.750 1.624 1.500 1.376 1.250 1.000
0.866 1.26 1.62 1.95 2.25 2.77
0.736 1.07 1.37 1.65 1.91 2.36
0.325 0.444 0.537 0.609 0.666 0.736
0.325 0.444 0.537 0.609 0.666 0.736
0.664 0.644 0.625 0.607 0.590 0.559
0.647 0.878 1.05 1.18 1.26 1.33
7.5 4.8 3.5 2.7 2.2 1.5
2.250 2.250 2.250 2.250 2.250 2.250
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500
WALL WALL WALL WALL WALL WALL
2.000 1.874 1.750 1.626 1.500 1.250
0.981 1.43 1.85 2.23 2.60 3.23
0.834 1.22 1.57 1.90 2.21 2.75
0.473 0.653 0.798 0.915 1.01 1.14
0.420 0.580 0.709 0.813 0.897 1.01
0.753 0.732 0.713 0.694 0.676 0.643
0.942 1.29 1.57 1.78 1.94 2.10
8.5 5.5 4.0 3.1 2.5 1.8
2.375 2.375 2.375 2.375
OD × 0.188 OD × 0.250 OD × 0.375 OD × 0.500
WALL WALL WALL WALL
1.999 1.875 1.625 1.375
1.52 1.96 2.77 3.46
1.29 1.67 2.36 2.95
0.778 0.955 1.22 1.39
0.655 0.804 1.03 1.17
0.776 0.756 0.719 0.686
1.54 1.88 2.36 2.59
5.8 4.3 2.7 1.9
2.500 2.500 2.500 2.500 2.500 2.500 2.500 2.500
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750
WALL WALL WALL WALL WALL WALL WALL WALL
2.250 2.124 2.000 1.876 1.750 1.500 1.250 1.000
1.10 1.61 2.08 2.52 2.94 3.69 4.33 4.85
0.933 1.37 1.77 2.14 2.50 3.14 3.68 4.12
0.659 0.918 1.13 1.31 1.46 1.67 1.80 1.87
0.528 0.735 0.906 1.05 1.17 1.34 1.44 1.49
0.841 0.820 0.800 0.781 0.763 0.729 0.699 0.673
1.32 1.82 2.24 2.57 2.83 3.14 3.24 3.16
9.5 6.1 4.5 3.5 2.8 2.0 1.5 1.2
2.625 OD × 0.250 WALL
2.125
2.19
1.87
1.33
1.01
0.844
2.63
4.8
Designation 1.500 1.500 1.500 1.500 1.500 1.500 1.500
V-28
OD × 0.062 OD × 0.094 OD × 0.125 OD × 0.156 OD × 0.188 OD × 0.250 OD × 0.375
January 2010
Table 21 ROUND TUBES (Continued) Inside Diameter in.
Weight lb/ft
Area A in2
I in4
S in3
r in.
J in4
Rb /t
WALL WALL WALL WALL WALL WALL WALL WALL
2.500 2.374 2.250 2.126 2.000 1.750 1.500 1.250
1.21 1.78 2.31 2.81 3.29 4.16 4.91 5.54
1.03 1.51 1.96 2.39 2.80 3.53 4.17 4.71
0.890 1.25 1.55 1.80 2.02 2.35 2.56 2.69
0.647 0.908 1.13 1.31 1.47 1.71 1.86 1.95
0.929 0.908 0.888 0.869 0.850 0.815 0.783 0.755
1.78 2.48 3.07 3.55 3.95 4.47 4.71 4.71
10.5 6.8 5.0 3.9 3.2 2.3 1.7 1.3
2.875 OD × 0.250 WALL 2.875 OD × 0.500 WALL
2.375 1.875
2.42 4.39
2.06 3.73
1.79 2.75
1.25 1.91
0.932 0.858
3.55 5.26
5.3 2.4
3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000
WALL WALL WALL WALL WALL WALL WALL WALL
2.750 2.624 2.500 2.250 2.000 1.750 1.500 1.000
1.33 1.95 2.54 3.64 4.62 5.48 6.23 7.39
1.13 1.66 2.16 3.09 3.93 4.66 5.30 6.28
1.17 1.65 2.06 2.72 3.19 3.52 3.73 3.93
0.779 1.10 1.37 1.81 2.13 2.34 2.49 2.62
1.02 0.996 0.976 0.938 0.901 0.868 0.839 0.791
2.33 3.28 4.08 5.33 6.14 6.58 6.71 6.28
11.5 7.5 5.5 3.5 2.5 1.9 1.5 1.0
3.250 OD × 0.250 WALL 3.250 OD × 0.375 WALL 3.250 OD × 0.500 WALL
2.750 2.500 2.250
2.77 3.98 5.08
2.36 3.39 4.32
2.67 3.56 4.22
1.64 2.19 2.60
1.06 1.03 0.988
5.30 7.00 8.17
6.0 3.8 2.8
3.500 3.500 3.500 3.500 3.500 3.500 3.500
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500 OD × 0.750
WALL WALL WALL WALL WALL WALL WALL
3.250 3.124 3.000 2.876 2.750 2.500 2.000
1.56 2.30 3.00 3.67 4.33 5.54 7.62
1.33 1.96 2.55 3.12 3.68 4.71 6.48
1.89 2.69 3.39 4.01 4.56 5.45 6.58
1.08 1.54 1.94 2.29 2.61 3.11 3.76
1.19 1.17 1.15 1.13 1.11 1.08 1.01
3.77 5.36 6.74 7.94 8.99 10.6 12.3
13.5 8.8 6.5 5.1 4.2 3.0 1.8
3.750 3.750 3.750 3.750 3.750
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.375 OD × 0.500
WALL WALL WALL WALL WALL
3.500 3.374 3.250 3.000 2.750
1.67 2.47 3.23 4.68 6.00
1.42 2.10 2.75 3.98 5.11
2.34 3.35 4.23 5.73 6.90
1.25 1.78 2.26 3.06 3.68
1.28 1.26 1.24 1.20 1.16
4.68 6.67 8.42 11.3 13.5
14.5 9.5 7.0 4.5 3.3
4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750
WALL WALL WALL WALL WALL WALL WALL WALL
3.750 3.624 3.500 3.376 3.250 3.000 2.750 2.500
1.79 2.65 3.46 4.25 5.02 6.47 7.79 9.01
1.52 2.25 2.95 3.61 4.27 5.50 6.63 7.66
2.86 4.10 5.20 6.19 7.09 8.59 9.76 10.6
1.43 2.05 2.60 3.09 3.54 4.30 4.88 5.32
1.37 1.35 1.33 1.31 1.29 1.25 1.21 1.18
5.71 8.18 10.4 12.3 14.0 16.8 18.9 20.2
15.5 10.1 7.5 5.9 4.8 3.5 2.7 2.2
4.250 4.250 4.250 4.250
OD × 0.125 OD × 0.250 OD × 0.375 OD × 0.500
WALL WALL WALL WALL
4.000 3.750 3.500 3.250
1.90 3.69 5.37 6.93
1.62 3.14 4.57 5.89
3.45 6.31 8.65 10.5
1.62 2.97 4.07 4.96
1.46 1.42 1.38 1.34
6.89 12.6 17.1 20.7
16.5 8.0 5.2 3.8
Designation 2.750 2.750 2.750 2.750 2.750 2.750 2.750 2.750
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750 OD × 1.000
January 2010
V-29
Table 21 ROUND TUBES (Continued) Designation
Inside Diameter in.
Weight lb/ft
Area A in2
I in4
S in3
r in.
J in4
Rb /t
4.500 4.500 4.500 4.500 4.500 4.500 4.500 4.500 4.500
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750 OD × 1.000
WALL WALL WALL WALL WALL WALL WALL WALL WALL
4.250 4.124 4.000 3.876 3.750 3.500 3.250 3.000 2.500
2.02 2.99 3.93 4.83 5.71 7.39 8.95 10.4 12.9
1.72 2.55 3.34 4.10 4.86 6.28 7.61 8.84 11.0
4.11 5.93 7.56 9.05 10.4 12.8 14.7 16.2 18.2
1.83 2.64 3.36 4.02 4.63 5.67 6.51 7.18 8.09
1.55 1.53 1.51 1.48 1.46 1.43 1.39 1.35 1.29
8.22 11.8 15.1 18.0 20.7 25.1 28.6 31.1 33.7
17.5 11.5 8.5 6.7 5.5 4.0 3.1 2.5 1.8
4.750 4.750 4.750 4.750 4.750
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.375 OD × 0.500
WALL WALL WALL WALL WALL
4.500 4.374 4.250 4.000 3.750
2.14 3.17 4.16 6.06 7.85
1.82 2.69 3.53 5.15 6.68
4.86 7.02 8.97 12.4 15.3
2.05 2.96 3.78 5.23 6.43
1.64 1.61 1.59 1.55 1.51
9.71 14.0 17.9 24.7 30.1
18.5 12.1 9.0 5.8 4.3
5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000 5.000
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750 OD × 1.000
WALL WALL WALL WALL WALL WALL WALL WALL WALL
4.750 4.624 4.500 4.376 4.250 4.000 3.750 3.500 3.000
2.25 3.34 4.39 5.40 6.41 8.31 10.1 11.8 14.8
1.91 2.84 3.73 4.60 5.45 7.07 8.59 10.0 12.6
5.69 8.24 10.6 12.7 14.7 18.1 21.0 23.3 26.7
2.28 3.30 4.22 5.07 5.87 7.25 8.39 9.33 10.7
1.72 1.70 1.68 1.66 1.64 1.60 1.56 1.53 1.46
11.4 16.5 21.0 25.2 29.1 35.8 41.1 45.2 50.3
19.5 12.8 9.5 7.5 6.2 4.5 3.5 2.8 2.0
5.500 5.500 5.500 5.500 5.500 5.500 5.500
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.375 OD × 0.500 OD × 0.750 OD × 1.000
WALL WALL WALL WALL WALL WALL WALL
5.250 5.124 5.000 4.750 4.500 4.000 3.500
2.48 3.69 4.85 7.10 9.24 13.2 16.6
2.11 3.14 4.12 6.04 7.85 11.2 14.1
7.63 11.1 14.2 19.9 24.8 32.4 37.6
2.77 4.03 5.18 7.25 9.01 11.8 13.7
1.90 1.88 1.86 1.82 1.78 1.70 1.63
15.2 22.1 28.4 39.6 49.1 63.1 71.6
21.5 14.1 10.5 6.8 5.0 3.2 2.3
6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000 6.000
OD × 0.125 OD × 0.188 OD × 0.250 OD × 0.312 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750 OD × 1.000
WALL WALL WALL WALL WALL WALL WALL WALL WALL
5.750 5.624 5.500 5.376 5.250 5.000 4.750 4.500 4.000
2.71 4.04 5.31 6.56 7.79 10.2 12.4 14.5 18.5
2.31 3.43 4.52 5.58 6.63 8.64 10.6 12.4 15.7
9.96 14.5 18.7 22.6 26.3 32.9 38.6 43.5 51.1
3.32 4.84 6.23 7.54 8.78 11.0 12.9 14.5 17.0
2.08 2.06 2.03 2.01 1.99 1.95 1.91 1.88 1.80
19.9 29.0 37.3 45.1 52.4 65.3 76.2 85.2 98.2
23.5 15.5 11.5 9.1 7.5 5.5 4.3 3.5 2.5
6.500 6.500 6.500 6.500
OD × 0.250 OD × 0.375 OD × 0.500 OD × 0.750
WALL WALL WALL WALL
6.000 5.750 5.500 5.000
5.77 8.49 11.1 15.9
4.91 7.22 9.42 13.5
24.0 34.0 42.7 56.9
7.39 10.5 13.1 17.5
2.21 2.17 2.13 2.05
47.9 67.7 84.8 112
12.5 8.2 6.0 3.8
6.750 OD × 0.500 WALL 6.750 OD × 0.750 WALL
5.750 5.250
11.5 16.6
9.82 14.1
48.2 64.6
14.3 19.1
2.22 2.14
95.9 127
6.3 4.0
V-30
January 2010
Table 21 ROUND TUBES (Continued) Inside Diameter in.
Weight lb/ft
Area A in2
I in4
S in3
r in.
J in4
Rb /t
WALL WALL WALL WALL WALL
6.500 6.250 6.000 5.500 5.000
6.23 9.18 12.0 17.3 22.2
5.30 7.80 10.2 14.7 18.8
30.2 43.0 54.2 72.9 87.2
8.64 12.3 15.5 20.8 24.9
2.39 2.35 2.30 2.23 2.15
60.4 85.6 108 144 170
13.5 8.8 6.5 4.2 3.0
7.500 OD × 0.250 WALL 7.500 OD × 0.375 WALL 7.500 OD × 0.500 WALL
7.000 6.750 6.500
6.70 9.87 12.9
5.69 8.39 11.0
37.5 53.4 67.7
9.99 14.2 18.1
2.56 2.52 2.48
74.8 107 135
14.5 9.5 7.0
8.000 8.000 8.000 8.000 8.000 8.000 8.000
WALL WALL WALL WALL WALL WALL WALL
7.750 7.500 7.250 7.000 6.750 6.500 6.000
3.64 7.16 10.6 13.9 17.0 20.1 25.9
3.09 6.09 8.98 11.8 14.5 17.1 22.0
24.0 45.7 65.4 83.2 99.2 113 137
5.99 11.4 16.4 20.8 24.8 28.4 34.4
2.78 2.74 2.70 2.66 2.62 2.58 2.50
47.9 91.4 131 166 197 224 269
31.5 15.5 10.2 7.5 5.9 4.8 3.5
8.500 OD × 0.250 WALL
8.000
7.62
6.48
55.2
13.0
2.92
110
16.5
9.000 OD × 0.250 WALL 9.000 OD × 0.375 WALL 9.000 OD × 0.500 WALL
8.500 8.250 8.000
8.08 11.9 15.7
6.87 10.2 13.4
65.8 94.7 121
14.6 21.0 26.9
3.09 3.05 3.01
132 189 241
17.5 11.5 8.5
Designation 7.000 7.000 7.000 7.000 7.000
OD × 0.250 OD × 0.375 OD × 0.500 OD × 0.750 OD × 1.000
OD × 0.125 OD × 0.250 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750 OD × 1.000
10.000 10.000 10.000 10.000 10.000 10.000
OD × 0.250 OD × 0.375 OD × 0.500 OD × 0.625 OD × 0.750 OD × 1.000
WALL WALL WALL WALL WALL WALL
9.500 9.250 9.000 8.750 8.500 8.000
9.01 13.3 17.5 21.6 25.6 33.3
7.66 11.3 14.9 18.4 21.8 28.3
91.1 132 169 203 235 290
18.2 26.3 33.8 40.6 46.9 58.0
3.45 3.41 3.36 3.32 3.28 3.20
182 263 337 404 466 573
19.5 12.8 9.5 7.5 6.2 4.5
10.500 10.500 10.500 10.500
OD × 0.250 OD × 0.375 OD × 0.500 OD × 0.750
WALL WALL WALL WALL
10.000 9.750 9.500 9.000
9.47 14.0 18.5 27.0
8.05 11.9 15.7 23.0
106 153 197 275
20.1 29.2 37.5 52.3
3.63 3.58 3.54 3.46
211 306 393 546
20.5 13.5 10.0 6.5
11.000 11.000 11.000 11.000
OD × 0.375 OD × 0.500 OD × 0.750 OD × 1.000
WALL WALL WALL WALL
10.250 10.000 9.500 9.000
14.7 19.4 28.4 36.9
12.5 16.5 24.2 31.4
177 228 319 397
32.2 41.4 58.0 72.1
3.76 3.72 3.63 3.55
353 455 634 785
14.2 10.5 6.8 5.0
12.000 12.000 12.000 12.000 12.000
OD × 0.250 OD × 0.375 OD × 0.500 OD × 0.750 OD × 1.000
WALL WALL WALL WALL WALL
11.500 11.250 11.000 10.500 10.000
10.9 16.1 21.2 31.2 40.6
9.23 13.7 18.1 26.5 34.6
159 232 299 421 527
26.6 38.6 49.9 70.2 87.8
4.16 4.11 4.07 3.99 3.91
319 463 597 839 1045
23.5 15.5 11.5 7.5 5.5
1. Tube can be produced by different methods. Seamless tube is usually required for applications with internal pressure. 2. Users are encouraged to check availability with suppliers. Additional sizes and shapes may be available from suppliers. 3. Tolerances for extruded shapes are given in Aluminum Standards and Data.
January 2010
V-31
Table 22 PIPES Schedule No.
Outside Diameter OD in.
Inside Diameter ID in.
Wall Thickness t in.
1 1/2
5 10 40 80 160
1.900 1.900 1.900 1.900 1.900
1.770 1.682 1.610 1.500 1.338
0.065 0.109 0.145 0.200 0.281
0.441 0.721 0.940 1.26 1.68
2
5 10 40 80 160
2.375 2.375 2.375 2.375 2.375
2.245 2.157 2.067 1.939 1.687
0.065 0.109 0.154 0.218 0.344
2 1/2
5 10 40 80 160
2.875 2.875 2.875 2.875 2.875
2.709 2.635 2.469 2.323 2.125
3
5 10 40 80 160
3.500 3.500 3.500 3.500 3.500
3 1/2
5 10 40 80
4
Nominal Pipe Size
5
6
V-32
Weight2 lb/ft
Area A in2
I in4
S in3
r in.
Rb /t
0.375 0.613 0.799 1.07 1.43
0.158 0.247 0.310 0.391 0.482
0.166 0.260 0.326 0.412 0.508
0.649 0.634 0.623 0.605 0.581
14.1 8.2 6.1 4.3 2.9
0.555 0.913 1.26 1.74 2.58
0.472 0.776 1.07 1.48 2.19
0.315 0.499 0.666 0.868 1.16
0.265 0.420 0.561 0.731 0.980
0.817 0.802 0.787 0.766 0.728
17.8 10.4 7.2 4.9 3.0
0.083 0.120 0.203 0.276 0.375
0.856 1.22 2.00 2.65 3.46
0.728 1.04 1.70 2.25 2.95
0.710 0.987 1.53 1.92 2.35
0.494 0.687 1.06 1.34 1.64
0.988 0.975 0.947 0.924 0.894
16.8 11.5 6.6 4.7 3.3
3.334 3.260 3.068 2.900 2.624
0.083 0.120 0.216 0.300 0.438
1.05 1.50 2.62 3.55 4.95
0.891 1.27 2.23 3.02 4.21
1.30 1.82 3.02 3.89 5.04
0.744 1.04 1.72 2.23 2.88
1.21 1.20 1.16 1.14 1.09
20.6 14.1 7.6 5.3 3.5
4.000 4.000 4.000 4.000
3.834 3.760 3.548 3.364
0.083 0.120 0.226 0.318
1.20 1.72 3.15 4.33
1.02 1.46 2.68 3.68
1.96 2.76 4.79 6.28
0.98 1.38 2.39 3.14
1.39 1.37 1.34 1.31
23.6 16.2 8.3 5.8
5 10 40 80 120 160 5 10 40 80 120 160
4.500 4.500 4.500 4.500 4.500 4.500 5.563 5.563 5.563 5.563 5.563 5.563
4.334 4.260 4.026 3.826 3.624 3.438 5.345 5.295 5.047 4.813 4.563 4.313
0.083 0.120 0.237 0.337 0.438 0.531 0.109 0.134 0.258 0.375 0.500 0.625
1.35 1.94 3.73 5.18 6.57 7.79 2.20 2.69 5.06 7.19 9.35 11.4
1.15 1.65 3.17 4.41 5.59 6.62 1.87 2.29 4.30 6.11 7.95 9.70
2.81 3.96 7.23 9.61 11.7 13.3 6.95 8.43 15.2 20.7 25.7 30.0
1.25 1.76 3.21 4.27 5.18 5.90 2.50 3.03 5.45 7.43 9.25 10.8
1.56 1.55 1.51 1.48 1.44 1.42 1.93 1.92 1.88 1.84 1.80 1.76
26.6 18.3 9.0 6.2 4.6 3.7 25.0 20.3 10.3 6.9 5.1 4.0
5 10 40 80 120 160
6.625 6.625 6.625 6.625 6.625 6.625
6.407 6.357 6.065 5.761 5.501 5.187
0.109 0.134 0.280 0.432 0.562 0.719
2.62 3.21 6.56 9.88 12.6 15.7
2.23 2.73 5.58 8.40 10.7 13.3
11.8 14.4 28.1 40.5 49.6 59.0
3.58 4.35 8.50 12.2 15.0 17.8
2.30 2.30 2.25 2.19 2.15 2.10
29.9 24.2 11.3 7.2 5.4 4.1
January 2010
Table 22 PIPES (Continued) Nominal Pipe Size
Schedule No.
Outside Diameter OD in.
Inside Diameter ID in.
Wall Thickness t in.
Weight2 lb/ft
Area A in2
I in4
S in3
r in.
Rb /t
5 10 20 30 40 60 80 100 120 140 160 5 10 20 30 40 60 80 100 5 10 20 30 40 60 80
8.625 8.625 8.625 8.625 8.625 8.625 8.625 8.625 8.625 8.625 8.625 10.750 10.750 10.750 10.750 10.750 10.750 10.750 10.750 12.750 12.750 12.750 12.750 12.750 12.750 12.750
8.407 8.329 8.125 8.071 7.981 7.813 7.625 7.437 7.187 7.001 6.813 10.482 10.420 10.250 10.136 10.020 9.750 9.562 9.312 12.438 12.390 12.250 12.090 11.938 11.626 11.374
0.109 0.148 0.250 0.277 0.322 0.406 0.500 0.594 0.719 0.812 0.906 0.134 0.165 0.250 0.307 0.365 0.500 0.594 0.719 0.156 0.180 0.250 0.330 0.406 0.562 0.688
3.43 4.64 7.74 8.54 9.88 12.3 15.0 17.6 21.0 23.4 25.8 5.26 6.45 9.70 11.8 14.0 18.9 22.3 26.6 7.26 8.36 11.5 15.1 18.5 25.3 30.7
2.92 3.94 6.58 7.26 8.40 10.5 12.8 15.0 17.9 19.9 22.0 4.47 5.49 8.25 10.1 11.9 16.1 19.0 22.7 6.17 7.11 9.82 12.9 15.7 21.5 26.1
26.4 35.4 57.7 63.4 72.5 88.7 106 121 141 154 166 63.0 76.9 114 137 161 212 245 286 122 140 192 248 300 400 476
6.13 8.21 13.4 14.7 16.8 20.6 24.5 28.2 32.6 35.6 38.5 11.7 14.3 21.2 25.6 29.9 39.4 45.6 53.3 19.2 22.0 30.1 39.0 47.1 62.8 74.6
3.01 3.00 2.96 2.95 2.94 2.91 2.88 2.85 2.81 2.78 2.75 3.75 3.74 3.71 3.69 3.67 3.63 3.60 3.56 4.45 4.44 4.42 4.39 4.37 4.31 4.27
39.1 28.6 16.8 15.1 12.9 10.1 8.1 6.8 5.5 4.8 4.3 39.6 32.1 21.0 17.0 14.2 10.3 8.5 7.0 40.4 34.9 25.0 18.8 15.2 10.8 8.8
8
10
12
1. Sizes are in accordance with ASME Standards B36.10M and B36.19M 2. Weights are for 6061, with a density of 0.098 lb/in3 3. Check availability of shaded sizes with suppliers before using. Additional sizes and shapes may be available from suppliers. 4. Tolerances for extruded shapes are given in Aluminum Standards and Data.
January 2010
V-33
Table 23 SQUARE TUBES
V-34
Axis x-x, y-y
Designation
Depth width d in.
Thickness t in.
Weight lb/ft
Area A in2
Ix , Iy in4
Sx , Sy in3
rx , ry in.
J in4
RT 1 × 1 × .065 RT 1 × 1 × .095 RT 1 × 1 × .125
1.000 1.000 1.000
0.065 0.095 0.125
0.286 0.404 0.515
0.243 0.344 0.438
0.0356 0.0475 0.0570
0.0712 0.0949 0.114
0.383 0.371 0.361
0.0531 0.0704 0.0837
RT 1.25 × 1.25 × .065 RT 1.25 × 1.25 × .095 RT 1.25 × 1.25 × .125
1.250 1.250 1.250
0.065 0.095 0.125
0.362 0.516 0.662
0.308 0.439 0.563
0.0723 0.0982 0.120
0.116 0.157 0.192
0.485 0.473 0.462
0.108 0.146 0.178
RT 1.375 × 1.375 × .125
1.375
0.125
0.735
0.625
0.164
0.239
0.513
0.244
RT 1.5 × 1.5 × .065 RT 1.5 × 1.5 × .078 RT 1.5 × 1.5 × .095 RT 1.5 × 1.5 × .125 RT 1.5 × 1.5 × .250
1.500 1.500 1.500 1.500 1.500
0.065 0.078 0.095 0.125 0.250
0.439 0.522 0.628 0.809 1.47
0.373 0.444 0.534 0.688 1.25
0.128 0.150 0.176 0.218 0.339
0.171 0.200 0.235 0.291 0.451
0.586 0.581 0.575 0.564 0.520
0.192 0.224 0.263 0.325 0.488
RT 1.75 × 1.75 × .125
1.750
0.125
0.956
0.813
0.360
0.411
0.665
0.536
RT 2 × 2 × .095 RT 2 × 2 × .125 RT 2 × 2 × .156 RT 2 × 2 × .188 RT 2 × 2 × .250
2.000 2.000 2.000 2.000 2.000
0.095 0.125 0.156 0.188 0.250
0.851 1.10 1.35 1.60 2.06
0.724 0.938 1.15 1.36 1.75
0.439 0.552 0.657 0.754 0.911
0.439 0.552 0.657 0.754 0.911
0.779 0.767 0.755 0.744 0.722
0.657 0.824 0.978 1.12 1.34
RT 2.25 × 2.25 × .125
2.250
0.125
1.25
1.06
0.802
0.713
0.869
1.20
RT 2.5 × 2.5 × .125 RT 2.5 × 2.5 × .188 RT 2.5 × 2.5 × .250
2.500 2.500 2.500
0.125 0.188 0.250
1.40 2.04 2.65
1.19 1.74 2.25
1.12 1.56 1.92
0.896 1.25 1.54
0.971 0.947 0.924
1.67 2.32 2.85
RT 2.75 × 2.75 × .125 RT 2.75 × 2.75 × .188
2.750 2.750
0.125 0.188
1.54 2.27
1.31 1.93
1.51 2.12
1.10 1.54
1.07 1.05
2.26 3.16
RT 3 × 3 × .095 RT 3 × 3 × .125 RT 3 × 3 × .188 RT 3 × 3 × .250 RT 3 × 3 × .375
3.000 3.000 3.000 3.000 3.000
0.095 0.125 0.188 0.250 0.375
1.30 1.69 2.49 3.23 4.63
1.10 1.44 2.11 2.75 3.94
1.55 1.98 2.80 3.49 4.61
1.04 1.32 1.87 2.33 3.08
1.19 1.17 1.15 1.13 1.08
2.33 2.97 4.18 5.20 6.78
RT 3.5 × 3.5 × .125 RT 3.5 × 3.5 × .250 RT 3.5 × 3.5 × .375
3.500 3.500 3.500
0.125 0.250 0.375
1.98 3.82 5.51
1.69 3.25 4.69
3.21 5.76 7.74
1.83 3.29 4.42
1.38 1.33 1.28
4.81 8.58 11.4
RT 4 × 4 × .125 RT 4 × 4 × .188 RT 4 × 4 × .250 RT 4 × 4 × .375 RT 4 × 4 × .500
4.000 4.000 4.000 4.000 4.000
0.125 0.188 0.250 0.375 0.500
2.28 3.37 4.41 6.39 8.23
1.94 2.87 3.75 5.44 7.00
4.85 6.96 8.83 12.0 14.6
2.43 3.48 4.41 6.02 7.29
1.58 1.56 1.53 1.49 1.44
7.27 10.4 13.2 17.9 21.4
January 2010
Table 23 SQUARE TUBES (Continued)
Designation
Depth width d in.
Thickness t in.
RT 6 × 6 × .125 RT 6 × 6 × .188 RT 6 × 6 × .250 RT 6 × 6 × .375 RT 6 × 6 × .500
6.000 6.000 6.000 6.000 6.000
RT 8 × 8 × .188 RT 8 × 8 × .250 RT 8 × 8 × .375 RT 8 × 8 × .500
8.000 8.000 8.000 8.000
Axis x-x, y-y
Weight lb/ft
Area A in2
Ix , Iy in4
Sx , Sy in3
0.125 0.188 0.250 0.375 0.500
3.45 5.14 6.76 9.92 12.9
2.94 4.37 5.75 8.44 11.0
16.9 24.6 31.7 44.7 55.9
5.64 8.21 10.6 14.9 18.6
2.40 2.37 2.35 2.30 2.25
25.3 36.9 47.5 66.7 83.2
0.188 0.250 0.375 0.500
6.91 9.11 13.5 17.6
5.87 7.75 11.4 15.0
59.8 77.7 111 141
14.9 19.4 27.8 35.3
3.19 3.17 3.12 3.07
89.6 116 166 211
rx , ry in.
J in4
1. Users are encouraged to check availability with suppliers. Additional sizes and shapes may be available from suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
January 2010
V-35
V-36
January 2010
Width b in. 1.000 1.000 1.000 1.000 1.000 1.250 1.250 1.250 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.500 1.750 1.750 1.750 1.750 1.750 1.750 1.750 1.750 1.750 1.750 1.750
Designation
RT 1 × 1 1/2 × 1/8 RT 1 × 2 × 1/8 RT 1 × 2 1/2 × 1/8 RT 1 × 3 × 1/8 RT 1 × 4 × 1/8
RT 1 1/4 × 2 × 1/8 RT 1 1/4 × 2 1/2 × 1/8 RT 1 1/4 × 3 × 1/8
RT 1 1/2 × 1 3/4 × 1/8 RT 1 1/2 × 2 × 1/8 RT 1 1/2 × 2 × 1/4 RT 1 1/2 × 2 1/2 × 1/8 RT 1 1/2 × 3 × 1/8 RT 1 1/2 × 3 × 3/16 RT 1 1/2 × 4 × 1/8 RT 1 1/2 × 6 × 1/8
RT 1 3/4 × 2 × 1/8 RT 1 3/4 × 2 1/4 × 1/8 RT 1 3/4 × 2 1/2 × 1/8 RT 1 3/4 × 2 3/4 × 1/8 RT 1 3/4 × 3 × 1/8 RT 1 3/4 × 3 1/2 × 1/8 RT 1 3/4 × 4 × 1/8 RT 1 3/4 × 4 1/2 × 1/8 RT 1 3/4 × 5 × 1/8 RT 1 3/4 × 5 × 3/16 RT 1 3/4 × 6 × 1/8
2.000 2.250 2.500 2.750 3.000 3.500 4.000 4.500 5.000 5.000 6.000
1.750 2.000 2.000 2.500 3.000 3.000 4.000 6.000
2.000 2.500 3.000
1.500 2.000 2.500 3.000 4.000
Depth d in.
0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.188 0.125
0.125 0.125 0.250 0.125 0.125 0.188 0.125 0.125
0.125 0.125 0.125
0.125 0.125 0.125 0.125 0.125
Thickness t in.
1.03 1.10 1.18 1.25 1.32 1.47 1.62 1.76 1.91 2.82 2.21
0.882 0.956 1.76 1.10 1.25 1.82 1.54 2.13
0.882 1.03 1.18
0.662 0.809 0.956 1.10 1.40
Weight lb/ft
0.875 0.938 1.00 1.06 1.13 1.25 1.38 1.50 1.63 2.40 1.88
0.750 0.813 1.50 0.938 1.06 1.55 1.31 1.81
0.750 0.875 1.00
0.563 0.688 0.813 0.938 1.19
Area A in2
0.497 0.661 0.855 1.08 1.34 1.96 2.74 3.69 4.83 6.91 7.74
0.318 0.442 0.719 0.767 1.21 1.68 2.51 7.20
0.387 0.678 1.08
0.159 0.332 0.590 0.950 2.04
Ix in4
Table 24 RECTANGULAR TUBES
0.497 0.588 0.684 0.785 0.892 1.12 1.37 1.64 1.93 2.76 2.58
0.364 0.442 0.719 0.613 0.806 1.12 1.25 2.40
0.387 0.543 0.720
0.212 0.332 0.472 0.633 1.02
Sx in3
Axis x-x
0.753 0.840 0.925 1.01 1.09 1.25 1.41 1.57 1.72 1.70 2.03
0.652 0.737 0.692 0.904 1.07 1.04 1.38 1.99
0.718 0.881 1.04
0.532 0.695 0.852 1.01 1.31
rx in.
0.401 0.442 0.484 0.525 0.566 0.649 0.732 0.814 0.897 1.23 1.06
0.248 0.278 0.438 0.337 0.396 0.533 0.515 0.752
0.180 0.219 0.259
0.0811 0.105 0.129 0.153 0.201
Iy in4
0.458 0.506 0.553 0.600 0.647 0.742 0.836 0.931 1.03 1.41 1.21
0.331 0.370 0.583 0.449 0.528 0.711 0.686 1.00
0.288 0.351 0.415
0.162 0.210 0.258 0.307 0.403
Sy in3
Axis y-y
0.677 0.687 0.696 0.703 0.710 0.721 0.730 0.737 0.743 0.717 0.753
0.575 0.585 0.540 0.599 0.611 0.586 0.626 0.644
0.489 0.501 0.509
0.380 0.391 0.399 0.404 0.412
ry in.
0.663 0.795 0.931 1.07 1.21 1.50 1.80 2.11 2.41 3.33 3.04
0.416 0.511 0.798 0.711 0.919 1.24 1.35 2.25
0.371 0.510 0.654
0.161 0.245 0.332 0.422 0.605
J in4
January 2010
V-37
2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.000 2.500 2.500 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 3.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 4.000 5.000
Designation
RT 2 × 3 × 1/8 RT 2 × 3 × 1/4 RT 2 × 4 × 1/8 RT 2 × 4 × 3/16 RT 2 × 4 × 1/4 RT 2 × 5 × 1/8 RT 2 × 5 × 3/16 RT 2 × 5 × 1/4 RT 2 × 6 × 1/8 RT 2 × 6 × 3/16 RT 2 × 6 × 1/4 RT 2 × 8 × 1/8
RT 2 1/2 × 4 × 1/8 RT 2 1/2 × 5 × 1/8
RT 3 × 4 × 1/8 RT 3 × 4 × 3/16 RT 3 × 4 × 1/4 RT 3 × 4 × 3/8 RT 3 × 4 × 1/2 RT 3 × 5 × 1/8 RT 3 × 5 × 3/16 RT 3 × 5 × 1/4 RT 3 × 6 × 1/8 RT 3 × 6 × 3/16 RT 3 × 8 × 1/4
RT 4 × 5 × 1/4 RT 4 × 6 × 1/8 RT 4 × 6 × 3/16 RT 4 × 6 × 1/4 RT 4 × 6 × 1/2 RT 4 × 8 × 3/16 RT 4 × 8 × 1/4 RT 4 × 8 × 3/8 RT 4 × 8 × 1/2
RT 5 × 8 × 3/8
8.000
5.000 6.000 6.000 6.000 6.000 8.000 8.000 8.000 8.000
4.000 4.000 4.000 4.000 4.000 5.000 5.000 5.000 6.000 6.000 8.000
4.000 5.000
3.000 3.000 4.000 4.000 4.000 5.000 5.000 5.000 6.000 6.000 6.000 8.000
Depth d in.
0.375
0.250 0.125 0.188 0.250 0.500 0.188 0.250 0.375 0.500
0.125 0.188 0.250 0.375 0.500 0.125 0.188 0.250 0.125 0.188 0.250
0.125 0.125
0.125 0.250 0.125 0.188 0.250 0.125 0.188 0.250 0.125 0.188 0.250 0.125
Thickness t in.
10.8
5.00 2.87 4.26 5.59 10.6 5.14 6.76 9.92 12.9
1.98 2.93 3.82 5.51 7.06 2.28 3.37 4.41 2.57 3.81 6.17
1.84 2.13
1.40 2.65 1.69 2.49 3.23 1.98 2.93 3.82 2.28 3.37 4.41 2.87
Weight lb/ft
9.19
4.25 2.44 3.62 4.75 9.00 4.37 5.75 8.44 11.0
1.69 2.49 3.25 4.69 6.00 1.94 2.87 3.75 2.19 3.24 5.25
1.56 1.81
1.19 2.25 1.44 2.11 2.75 1.69 2.49 3.25 1.94 2.87 3.75 2.44
Area A in2
78.4
15.1 12.6 18.3 23.5 40.8 36.8 47.6 67.5 84.9
3.92 5.59 7.07 9.56 11.5 6.69 9.63 12.3 10.4 15.1 40.1
3.45 5.95
1.47 2.55 2.98 4.23 5.31 5.20 7.45 9.44 8.28 11.9 15.2 17.5
Ix in4
19.6
6.04 4.20 6.09 7.82 13.6 9.21 11.9 16.9 21.2
1.96 2.80 3.53 4.78 5.75 2.68 3.85 4.91 3.48 5.03 10.0
1.72 2.38
0.978 1.70 1.49 2.11 2.65 2.08 2.98 3.78 2.76 3.98 5.07 4.36
Sx in3
Axis x-x
1. Users are encouraged to check availability with suppliers. Additional sizes and shapes may be available from suppliers. 2. Tolerances for extruded shapes are given in Aluminum Standards and Data.
Width b in.
2.92
1.88 2.27 2.25 2.22 2.13 2.90 2.88 2.83 2.78
1.52 1.50 1.47 1.43 1.38 1.86 1.83 1.81 2.18 2.16 2.76
1.48 1.81
1.11 1.06 1.44 1.41 1.39 1.76 1.73 1.70 2.07 2.04 2.01 2.68
rx in.
37.0
10.6 6.73 9.69 12.3 20.8 12.4 15.9 21.9 26.9
2.50 3.54 4.44 5.92 7.00 3.02 4.29 5.39 3.53 5.03 8.23
1.65 2.00
0.772 1.30 0.992 1.37 1.68 1.21 1.68 2.07 1.43 1.99 2.45 1.87
Iy in4
14.8
5.29 3.37 4.85 6.17 10.4 6.21 7.93 11.0 13.5
1.67 2.36 2.96 3.94 4.67 2.01 2.86 3.59 2.36 3.35 5.49
1.32 1.60
0.77 1.30 0.992 1.37 1.68 1.21 1.68 2.07 1.43 1.99 2.45 1.87
Sy in3
Axis y-y
2.01
1.58 1.66 1.64 1.61 1.52 1.69 1.66 1.61 1.56
1.22 1.19 1.17 1.12 1.08 1.25 1.22 1.20 1.27 1.25 1.25
1.03 1.05
0.806 0.759 0.831 0.806 0.782 0.847 0.822 0.798 0.860 0.834 0.809 0.876
ry in.
76.1
18.7 13.3 19.2 24.5 41.2 28.7 36.7 50.9 62.6
4.60 6.52 8.18 10.9 12.8 6.34 9.03 11.4 8.15 11.6 21.6
3.39 4.62
1.53 2.57 2.30 3.19 3.92 3.09 4.32 5.32 3.91 5.47 6.75 5.59
J in4
Table 25 ROOFING AND SIDING – DIMENSIONS AND WEIGHTS
V-38
January 2010
Table 26 ROOFING AND SIDING – SECTION PROPERTIES
January 2010
V-39
Table 27 DECIMAL EQUIVALENTS IN INCHES OF SHEET METAL AND WIRE GAUGES
V-40
January 2010
Table 28 GEOMETRIC SHAPES
January 2010
V-41
Table 28 GEOMETRIC SHAPES (Continued)
V-42
January 2010
Table 28 GEOMETRIC SHAPES (Continued)
January 2010
V-43
Table 28 GEOMETRIC SHAPES (Continued) ANGLE Y Z
x
W
α
d
c
X
X
y
W
t
Y
t
a b Z
z-z axis is axis of minimum I
x=
b 2 + ct 2(b + c )
y=
d 2 + at 2(b + c )
Ix =
t (d − y ) + by 3 − a ( y − t ) 3
Iy =
K=
abcdt 4(b + c )
α = (1 / 2 ) tan −1
3
t (b − x ) + dx 3 − c( x − t ) 3
3
3
3
2K Iy − Ix
I z = I x sin 2 α + I y cos 2 α + K sin 2α
I x + Iy = Iw + Iz I w = I x cos 2 α + I y sin 2 α − K sin 2α xo = x − t / 2 wo = y o sin α + x o cos α b' = d − t / 2
yo = y − t / 2 z o = y o cos α − x o sin α d'= b − t / 2
] ( ] (
)
xo y − ( y o − b') y y o 2 − ( y o − b ') 2 + o + o x o 3 − ( x o − d ') 3 + y o 3 d ' 2 4 3 2 4 4 ( ) ' yo x − x − d x o C2 = x o 2 − ( x o − d ') 2 + o + o y o 3 − ( y o − b')3 + x o 3 b' 2 4 3 t (C1 cos α − C 2 sin α ) βw = − 2z o Iw 2
C1 =
[
[
V-44
4
4
)
[
]
[
]
January 2010
Aluminum Design Manual
PART VI Design Aids
VI Design Aids TABLE OF CONTENTS Buckling Constants Table 1-1 Buckling Constants (unwelded). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1-2 Buckling Constants (welded) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Allowable Stresses for Building-Type Structures Table 2-1 1100-H14 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2-2 3003-H14 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2-3 3003-H16 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2-4 Alclad 3004-H34 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2-5 5005-H14 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2-6 5005-H32 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2-7 5005-H34 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2-8 5050-H34 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2-9 5052-H32 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2-10 5052-H34 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2-11 5052-H36 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2-12 5083-H116, H32, H321 Sheet and Plate (0.188 to 1.500 in. thick). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2-13 5086-H34 Sheet and Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2-14 5086-H116 Sheet and Plate, 5086-H32 Drawn Tube, Sheet and Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2-15 5454-H32 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2-16 5454-H34 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2-17 6005A-T61 Extrusions (up through 1.000 in. thick) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2-18 6061-T6 Sheet, -T651 Plate (up through 4.000 in. thick), 6061-T6 Rolled or Cold Finished Rod and Bar, 6061-T6 Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2-19 6061-T6, T6510, T6511 Extrusions, 6061-T6 Pipe, 6351-T5 Extrusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2-20 6063-T5 Extrusions (up through 0.500 in. thick), 6063-T52 Extrusions (up through 1.000 in. thick). . . . . . . 29 2-21 6063-T6 Extrusions and Pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2-22 6082-T6, -T6511 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2-23 6351-T6 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2-24 7005-T53 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2-1W 1100-H14 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2-2W 3003-H14 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2-3W 3003-H16 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2-4W Alclad 3004-H34 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2-5W 5005-H14 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2-6W 5005-H32 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2-7W 5005-H34 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2-8W 5050-H34 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2-9W 5052-H32 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2-10W 5052-H34 Sheet, Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2-11W 5052-H36 Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2-12W 5083-H116, H32, H321 Sheet and Plate (0.188 to 1.500 in. thick). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2-13W 5086-H34 Sheet and Plate, Drawn Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2-14W 5086-H116 Sheet and Plate, 5086-H32 Drawn Tube, Sheet and Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2-15W 5454-H32 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2-16W 5454-H34 Sheet and Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2-17W 6005A-T61 Extrusions (up through 1.000 in. thick) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2-18W 6061-T6, T651, T6510, T6511 All Products, welded with 4043, 5554, or 5654 and > 0.375 in. thick. . . . . . . 51 2-19W 6061-T6, T651, T6510, T6511 All Products welded with 5183, 5356, or 5556, or welded with 4043, 5554, 5654 and ≤ 0.375 in. thick. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
January 2010
VI-3
2-20W 2-21W 2-22W 2-23W 2-24W
Bending Table 3-1 3-2 3-3 3-4
6063-T5 Extrusions (up through 0.500 in. thick), 6063-T52 Extrusions (up through 1.000 in. thick). . . . . . . 53 6063-T6 Extrusions and Pipe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 6082-T6, -T6511 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 6351-T6 Extrusions welded with 4043, 5554, or 5654 and > 0.375 in. thick . . . . . . . . . . . . . . . . . . . . . . . . . . 56 7005-T53 Extrusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Recommended Minimum Bend Radii for 90o Cold Bends, Sheet and Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . 58 Recommended Minimum Inside Radii for 180o Cold Bends, Wire and Rod. . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Sheet Thickness for 180o Cold Bending (Metal to Metal). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 Developed Length of Material for 90o Bends. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Allowable Loads Table 4-1 Allowable Uniform Beam Loads: Aluminum Association Standard Channels, Alloy 6061-T6 . . . . . . . . . . . . 63 4-2 Allowable Uniform Beam Loads: Aluminum Association Standard I-Beams, Alloy 6061-T6. . . . . . . . . . . . . 64 4-3 Allowable Loads on Aluminum Tread Plate. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4-4 Maximum Spans: Commercial Corrugated and V-Beam Roofing and Siding. . . . . . . . . . . . . . . . . . . . . . . . . . 66 4-5 Maximum Spans: Commercial Ribbed Siding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Fasteners Table 5-1 5-2 5-3 5-4 5-5 5-6
Nominal Tensile And Single Shear Strengths for 2024-T4 and 7075-T73 Machine Screws. . . . . . . . . . . . . . . 69 Nominal Single Shear Strengths for 2024-T4 And 7075-T73 Type AB and B Sheet Metal Screws. . . . . . . . . 70 Nominal Tensile and Single Shear Strengths for 2024-T4 and 7075-T73 Bolts And Cap Screws . . . . . . . . . . 70 Bolt Dimensions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Nut Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Internal Thread Stripping Area for Class 2B UNC Threads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Welds Table 6-1 ASD Allowable Tensile Stresses for Groove Welds (Building-Type Structures). . . . . . . . . . . . . . . . . . . . . . . . 74 6-1M ASD Allowable Tensile Stresses for Groove Welds (Building-Type Structures). . . . . . . . . . . . . . . . . . . . . . . . 75 6-2 ASD Allowable Shear Stresses for Fillet Welds (Building-Type Structures). . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6-2M ASD Allowable Shear Stresses for Fillet Welds (Building-Type Structures). . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6-3 LRFD Design Tensile Stresses for Groove Welds (Building-Type Structures). . . . . . . . . . . . . . . . . . . . . . . . . 78 6-3M LRFD Design Tensile Stresses for Groove Welds (Building-Type Structures). . . . . . . . . . . . . . . . . . . . . . . . . 79 6-4 LRFD Design Shear Stresses for Fillet Welds (Building-Type Structures). . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 6-4M LRFD Design Shear Stresses for Fillet Welds (Building-Type Structures) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Beam Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82
VI-4
January 2010
January 2010
VI-5
Sheet Plate Extrusions Rod & Bar, Drawn Tube
2014 T6 T651 T6, T6510, T6511 T6, T651
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube
3004 H32 H34 H36 H38 H34 H36
3005 H25 H28
Sheet Sheet
Sheet Sheet Sheet Sheet Sheet Sheet
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube
Alclad 3003 H12 H14 H16 H18 H14 H18
Alclad 3004 H32 H34 H36 H38 H131, H241, H341 H151, H261, H361
Sheet & Plate Sheet & Plate Sheet Sheet Drawn Tube Drawn Tube Drawn Tube Drawn Tube
3003 H12 H14 H16 H18 H12 H14 H16 H18
Sheet Sheet Plate
Sheet, Plate, Drawn Tube, Rod & Bar Sheet, Plate, Drawn Tube, Rod & Bar
1100 H12 H14
Alclad 2014 T6 T6 T651
Product*
Alloy Temper
0.013 to 0.050 0.006 to 0.080
0.017 to 0.249 0.009 to 0.249 0.006 to 0.162 0.006 to 0.128 0.024 to 0.050 0.024 to 0.050
0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 0.018 to 0.450 0.018 to 0.450
0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 0.025 to 0.259 0.010 to 0.500
0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.006 to 0.128 All All All All
0.025 to 0.039 0.040 to 0.249 0.250 to 0.499
22.8 29.0
19.2 24.0 27.7 32.7 25.3 32.7
20.4 25.3 29.0 33.9 27.7 31.4
9.9 14.5 19.2 21.6 16.8 22.8
11.0 15.7 20.4 22.8 12.2 18.0 21.6 24.0
64.8 67.3 64.8
68.6 67.3 59.9 61.1
14.5
All 0.040 to 0.249 0.250 to 2.000 All All
11.0
Bc ksi
All
Thickness in.
Cc
165 138 121 114 157 129 118 112
53 52 53
52 52 55 55
121 109 102 94 104 98
0.133 0.190
114 102
0.103 125 0.144 112 0.178 104 0.228 96 0.155 109 0.228 96
0.112 0.155 0.190 0.241 0.178 0.215
0.038 174 0.067 144 0.103 125 0.123 118 0.084 133 0.133 114
0.044 0.075 0.112 0.133 0.052 0.093 0.123 0.144
0.502 0.531 0.502
0.544 0.529 0.444 0.458
0.067 144
0.044 165
Dc ksi
Dp ksi
0.673 0.655 0.548 0.566
0.132 0.187 0.232 0.299 0.201 0.299
0.145 0.201 0.248 0.317 0.232 0.282
0.047 0.086 0.132 0.158 0.108 0.172
0.056 0.096 0.145 0.172 0.065 0.120 0.158 0.187
27.1 0.172 34.6 0.248
22.7 28.6 33.1 39.2 30.1 39.2
24.2 30.1 34.6 40.7 33.1 37.6
11.5 17.0 22.7 25.7 19.9 27.1
12.8 18.4 24.2 27.1 14.2 21.3 25.7 28.6
74.7 0.621 77.6 0.658 74.7 0.621
79.1 77.6 69.0 70.4
17.0 0.086
12.8 0.056
Bp ksi
105 93
115 102 95 87 100 87
111 100 93 86 95 89
162 133 115 108 123 105
153 127 111 105 145 119 108 102
49 48 49
48 49 52 51
133
153
Cp
26.3 33.2
22.2 27.7 31.8 37.4 29.1 37.4
23.5 29.1 33.2 38.8 31.8 36.0
11.4 16.8 22.2 24.9 19.5 26.3
12.7 18.1 23.5 26.3 14.1 20.8 24.9 27.7
70.4 73.0 70.4
74.3 73.0 65.2 66.5
16.8
12.7
Bt ksi
22.6
17.0
Bbr ksi
345 282 247 213 269 213
327 269 238 205 247 220
635 446 345 310 389 295
573 416 327 295 523 366 310 281
36.1 46.1
30.2 38.1 44.1 52.2 40.1 52.2
32.2 40.1 46.1 54.3 44.1 50.2
15.2 22.6 30.2 34.1 26.4 36.1
17.0 24.5 32.2 36.1 18.9 28.3 34.1 38.1
98 112.7 94 117.2 98 112.7
94 119.5 95 117.2 105 103.8 103 106.0
446
573
Ct
0.977 295 1.335 238
0.779 1.046 1.261 1.565 1.117 1.565
0.844 1.117 1.335 1.644 1.261 1.487
0.321 0.536 0.779 0.910 0.654 0.977
0.372 0.594 0.844 0.977 0.425 0.716 0.910 1.046
2.922 3.068 2.922
3.132 3.058 2.628 2.699
0.536
0.372
Dt ksi
Table 1-1 BUCKLING CONSTANTS (UNWELDED)
0.264 0.382
0.203 0.287 0.357 0.460 0.309 0.460
0.223 0.309 0.382 0.488 0.357 0.433
0.072 0.131 0.203 0.243 0.165 0.264
0.086 0.148 0.223 0.264 0.100 0.184 0.243 0.287
1.410 1.496 1.410
1.532 1.489 1.240 1.280
0.131
0.086
Dbr ksi
91 81
99 89 82 76 86 76
96 86 81 74 82 77
140 115 99 94 106 91
133 111 96 91 126 103 94 89
53 52 53
52 52 56 55
115
133
Cbr
39.4 49.8
33.3 41.5 47.7 56.1 43.6 56.1
35.3 43.6 49.8 58.2 47.7 54.0
17.1 25.1 33.3 37.4 29.2 39.4
19.1 27.1 35.3 39.4 21.1 31.2 37.4 41.5
105.6 109.5 105.6
111.5 109.5 97.7 99.7
25.1
19.1
Btb ksi
Ctb
172 133 111 102 121 99
160 127 106 99 150 115 102 95
42 41 42
41 41 44 44
2.300 3.142
1.833 2.462 2.968 3.682 2.628 3.682
99 85
111 95 87 78 92 78
1.985 106 2.628 92 3.142 85 3.868 76 2.968 87 3.499 80
0.756 1.261 1.833 2.141 1.539 2.300
0.875 1.398 1.985 2.300 0.999 1.684 2.141 2.462
8.362 8.779 8.362
8.962 8.752 7.521 7.723
1.261 133
0.875 160
Dtb ksi
0.081 0.109 0.133 0.158 0.125 0.158
0.088 0.117 0.141 0.167 0.117 0.141
0.031 0.056 0.081 0.102 0.056 0.102
0.035 0.062 0.088 0.109 0.035 0.062 0.088 0.109
0.285 0.302 0.302
0.370 0.318 0.267 0.283
0.045
0.031
Ds ksi
18.2 0.095 22.8 0.133
16.4 20.0 22.8 25.6 21.9 25.6
17.3 21.0 23.7 26.5 21.0 23.7
8.6 12.9 16.4 19.1 12.9 19.1
9.4 13.8 17.3 20.0 9.4 13.8 17.3 20.0
44.4 46.2 46.2
53.1 47.9 42.7 44.4
11.1
8.6
Bs ksi
128 115
135 122 115 108 117 108
131 120 112 106 120 112
187 152 135 125 152 125
178 147 131 122 178 147 131 122
64 63 63
59 62 66 64
164
187
Cs
VI-6
January 2010
Sheet & Plate Sheet & Plate Sheet Sheet & Plate Sheet & Plate Sheet Sheet Sheet Rod & Bar, Drawn Tube Rod & Bar, Drawn Tube Sheet & Plate Sheet & Plate, Rod & Bar, Drawn Tube Sheet Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Plate Extrusions Extrusions Sheet & Plate Plate Plate Plate Plate Sheet & Plate Sheet & Plate, Drawn Tube Sheet & Plate, Drawn Tube Sheet
5050 H32 H34 H32 H34
5052 O H32 H34 H36
5083 O H111 H111 O H116, H32, H321 H116, H32, H321
5086 O H111 O H112 H112 H112 H112 H116 H32
5154 H38
H34
Sheet
3105 H25
Product*
5005 H12 H14 H16 H32 H34 H36
Alloy Temper
0.006 to 0.128
All
up thru 5.000 up thru 5.000 0.020 to 2.000 0.025 to 0.499 0.500 to 1.000 1.001 to 2.000 2.001 to 3.000 All All
up thru 5.000 up thru 0.500 0.501 to 5.000 0.051 to 1.500 0.188 to 1.500 1.501 to 3.000
39.0
37.7
15.7 20.4 15.7 19.2 18.0 16.8 16.8 30.2 30.2
18.0 24.0 24.0 20.4 30.2 27.7
10.4 24.0 27.7 30.2
21.6
All 0.006 to 3.000 All All 0.006 to 0.162
15.7 20.4 16.8
14.5 16.8 20.4 12.2 15.7 18.0
19.2
Bc ksi
0.017 to 0.249 0.009 to 0.249 All
0.017 to 2.000 0.009 to 1.000 0.006 to 0.162 0.017 to 2.000 0.009 to 1.000 0.006 to 0.162
0.013 to 0.080
Thickness in. 144 133 121 157 138 129
125
Cc
118
0.294
0.278
0.074 0.111 0.074 0.101 0.092 0.083 0.083 0.199 0.199
88
90
140 123 140 127 131 135 135 101 101
0.092 131 0.142 113 0.142 113 0.111 123 0.199 101 0.175 105
0.041 170 0.143 112 0.177 104 0.201 100
0.123
0.075 138 0.112 121 0.084 133
0.067 0.084 0.112 0.052 0.075 0.093
0.103
Dc ksi
Dp ksi 0.086 0.108 0.145 0.065 0.096 0.120
0.095 0.143 0.095 0.130 0.118 0.106 0.106 0.261 0.261
0.118 0.184 0.184 0.143 0.261 0.229
0.051 0.186 0.231 0.263
46.9 0.388
45.4 0.367
18.4 24.2 18.4 22.7 21.3 19.9 19.9 36.1 36.1
21.3 28.6 28.6 24.2 36.1 33.1
12.1 28.6 33.1 36.1
25.7 0.158
18.4 0.096 24.2 0.145 19.9 0.108
17.0 19.9 24.2 14.2 18.4 21.3
22.7 0.132
Bp ksi
81
82
129 113 129 116 120 125 125 92 92
120 104 104 113 92 96
158 103 96 91
108
127 111 123
133 123 111 145 127 119
115
Cp
44.5
43.1
18.1 23.5 18.1 22.2 20.8 19.5 19.5 34.6 34.6
20.8 27.7 27.7 23.5 34.6 31.8
12.1 27.7 31.8 34.6
24.9
18.1 23.5 19.5
16.8 19.5 23.5 14.1 18.1 20.8
22.2
Bt ksi
Ct
446 389 327 523 416 366
427 336 421 355 375 400 400 235 235
376 289 289 336 235 254
608 284 250 231
1.957 184
1.869 192
0.588 0.835 0.588 0.771 0.709 0.648 0.648 1.397 1.397
0.709 1.036 1.036 0.835 1.397 1.249
0.345 1.043 1.257 1.406
0.910 310
0.594 416 0.844 327 0.654 389
0.536 0.654 0.844 0.425 0.594 0.716
0.779 345
Dt ksi
62.6
60.5
24.5 32.2 24.5 30.2 28.3 26.4 26.4 48.1 48.1
28.3 38.1 38.1 32.2 48.1 44.1
16.1 38.1 44.1 48.1
34.1
24.5 32.2 26.4
22.6 26.4 32.2 18.9 24.5 28.3
30.2
Bbr ksi
Table 1-1 BUCKLING CONSTANTS (UNWELDED) (Continued)
0.598
0.565
0.146 0.219 0.146 0.200 0.181 0.163 0.163 0.401 0.401
0.181 0.282 0.282 0.219 0.401 0.352
0.078 0.285 0.355 0.405
0.243
0.148 0.223 0.165
0.131 0.165 0.223 0.100 0.148 0.184
0.203
Dbr ksi
70
71
112 98 112 101 104 108 108 80 80
104 90 90 98 80 84
137 89 83 79
94
111 96 106
115 106 96 126 111 103
99
Cbr
66.7
64.6
27.1 35.3 27.1 33.3 31.2 29.2 29.2 51.9 51.9
31.2 41.5 41.5 35.3 51.9 47.7
18.1 41.5 47.7 51.9
37.4
27.1 35.3 29.2
25.1 29.2 35.3 21.1 27.1 31.2
33.3
Btb ksi
133 121 106 150 127 115
111
Ctb
4.605
4.397
1.385 1.966 1.385 1.815 1.668 1.524 1.524 3.287 3.287
71
73
129 108 129 113 118 123 123 84 84
1.668 118 2.438 97 2.438 97 1.966 108 3.287 84 2.939 89
0.812 167 2.454 96 2.958 88 3.308 83
2.141 102
1.398 127 1.985 106 1.539 121
1.261 1.539 1.985 0.999 1.398 1.684
1.833
Dtb ksi
Ds ksi 0.045 0.062 0.081 0.035 0.051 0.068
0.045 0.087 0.045 0.067 0.056 0.045 0.045 0.139 0.139
0.056 0.108 0.108 0.067 0.164 0.147
0.024 0.101 0.124 0.148
30.3 0.202
29.4 0.191
11.1 17.3 11.1 14.6 12.9 11.1 11.1 23.7 23.7
12.9 20.0 20.0 14.6 26.5 24.7
7.3 19.1 21.9 24.7
16.4 0.081
12.9 0.056 16.4 0.081 12.9 0.056
11.1 13.8 16.4 9.4 12.0 14.6
15.5 0.075
Bs ksi
100
102
166 133 166 145 155 166 166 114 114
155 124 124 145 108 112
203 126 118 111
135
152 135 152
164 147 135 178 158 143
139
Cs
January 2010
VI-7
Sheet & Plate Sheet & Plate Sheet & Plate Plate Plate Plate
5456 O H116 H32, H321 H116 H32, H321 H116, H32, H321
Sheet & Plate Extrusions Rod & Bar Drawn Tube Pipe Extrusions Extrusions Extrusions Extrusions & Pipe Extrusions Extrusions Extrusions Extrusions Extrusions Extrusions Extrusions Extrusions
6061 T6, T651 T6, T6510, T6511 T6, T651 T6 T6
6063 T5 T5 T52 T6
6066 T6, T6510, T6511
6070 T6, T62
6082 T6, T6511
6105 T5
6351 T5 6351 T6
6463 T6
7005 T53
Extrusions Extrusions
Extrusions Extrusions Extrusions Extrusions Sheet & Plate Sheet & Plate Sheet & Plate
5454 O H111 H111 H112 O H32 H34
6005 T5 6005A T61
Product*
Alloy Temper
51.4
51.4
17.3 16.2 17.3 27.6
39.4 39.4 39.4 39.4 39.4
39.4 39.4
21.6 31.4 31.4 29.0 29.0 29.0
13.3 18.0 18.0 14.5 13.3 27.7 31.4
Bc ksi
up thru 0.750
up thru 0.500
up thru 1.000 up thru 0.750
up thru 0.500
48.9
27.6
39.4 41.7
39.4
0.200 thru 6.000 42.9
up thru 2.999
All
up thru 0.500 0.500 to 1.000 up thru 1.000 All
0.010 to 4.000 All up thru 8.000 0.025 to 0.500 All
up thru 1.000 up thru 1.000
0.051 to 1.500 0.188 to 1.250 0.188 to 0.499 1.251 to 1.500 0.501 to 1.500 1.501 to 3.000
up thru 5.000 up thru 0.500 0.501 to 5.000 up thru 5.000 0.020 to 3.000 0.020 to 2.000 0.020 to 1.000
Thickness in.
66 66 66 66 66
66 66
119 99 99 103 103 103
152 131 131 146 152 105 99
Cc
0.334
0.145
0.246 0.268
0.246
0.280
0.366
0.366
60
78
66 64
66
63
57
57
0.072 99 0.065 102 0.072 99 0.145 78
0.246 0.246 0.246 0.246 0.246
0.246 0.246
0.121 0.212 0.212 0.187 0.187 0.187
0.058 0.092 0.092 0.066 0.058 0.175 0.212
Dc ksi
0.156 0.277 0.277 0.245 0.245 0.245
0.074 0.118 0.118 0.084 0.074 0.229 0.277
Dp ksi
0.086 0.077 0.086 0.175
0.300 0.300 0.300 0.300 0.300
56.2 0.411
31.4 0.175
45.0 0.300 47.8 0.329
45.0 0.300
49.2 0.343
59.0 0.451
59.0 0.451
19.5 18.2 19.5 31.4
45.0 45.0 45.0 45.0 45.0
45.0 0.300 45.0 0.300
25.7 37.6 37.6 34.6 34.6 34.6
15.6 21.3 21.3 17.0 15.6 33.1 37.6
Bp ksi
56
74
61 60
61
59
54
54
93 97 93 74
61 61 61 61 61
61 61
110 90 90 94 94 94
140 120 120 135 140 96 90
Cp
53.5
30.5
43.2 45.8
43.2
47.0
56.1
56.1
19.2 18.0 19.2 30.5
43.2 43.2 43.2 43.2 43.2
43.2 43.2
24.9 36.0 36.0 33.2 33.2 33.2
15.4 20.8 20.8 16.8 15.4 31.8 36.0
Bt ksi
499 227 227 244 244 244
495 376 376 458 495 254 227
Ct
275 290 275 189
141 141 141 141 141
2.045 121
0.978 189
1.558 141 1.682 134
1.558 141
1.745 131
2.206 112
2.206 112
0.529 0.484 0.529 0.978
1.558 1.558 1.558 1.558 1.558
1.558 141 1.558 141
0.901 1.473 1.473 1.322 1.322 1.322
0.475 0.709 0.709 0.531 0.475 1.249 1.473
Dt ksi
84.0
46.1
66.8 71.1
66.8
73.2
88.3
88.3
28.3 26.4 28.3 46.1
66.8 66.8 66.8 66.8 66.8
66.8 66.8
34.1 50.2 50.2 46.1 46.1 46.1
20.7 28.3 28.3 22.6 20.7 44.1 50.2
Bbr ksi
Table 1-1 BUCKLING CONSTANTS (UNWELDED) (Continued)
0.920
0.382
0.666 0.730
0.666
0.763
1.011
1.011
0.184 0.165 0.184 0.382
0.666 0.666 0.666 0.666 0.666
0.666 0.666
0.240 0.427 0.427 0.376 0.376 0.376
0.113 0.181 0.181 0.129 0.113 0.352 0.427
Dbr ksi
61
81
67 65
67
64
58
58
103 106 103 81
67 67 67 67 67
67 67
95 78 78 82 82 82
122 104 104 117 122 84 78
Cbr
80.2
45.7
64.8 68.6
64.8
70.6
84.1
84.1
28.8 26.9 28.8 45.7
64.8 64.8 64.8 64.8 64.8
64.8 64.8
37.4 54.0 54.0 49.8 49.8 49.8
23.1 31.2 31.2 25.1 23.1 47.7 54.0
Btb ksi
Ctb
55 55 55 55 55
55 55
5.852
2.800
4.458 4.814
4.458
4.995
6.313
6.313
49
70
55 53
55
52
47
47
1.513 95 1.384 100 1.513 95 2.800 70
4.458 4.458 4.458 4.458 4.458
4.458 4.458
2.120 104 3.465 82 3.465 82 3.112 86 3.112 86 3.112 86
1.117 144 1.668 118 1.668 118 1.249 136 1.117 144 2.939 89 3.465 82
Dtb ksi
0.073 0.182 0.182 0.164 0.164 0.147
0.035 0.073 0.073 0.035 0.035 0.123 0.147
Ds ksi
0.040 0.036 0.040 0.082
0.141 0.141 0.141 0.141 0.141
34.9 0.201
19.0 0.082
27.2 0.141 28.9 0.155
27.2 0.141
29.8 0.162
35.7 0.212
35.7 0.212
11.8 11.0 11.8 19.0
27.2 27.2 27.2 27.2 27.2
27.2 0.141 27.2 0.141
15.5 28.4 28.4 26.5 26.5 24.7
9.4 15.5 15.5 9.4 9.4 21.9 24.7
Bs ksi
71
95
79 77
79
76
69
69
120 124 120 95
79 79 79 79 79
79 79
141 104 104 108 108 112
181 141 141 181 181 119 112
Cs
VI-8
January 2010
Sheet & Plate, Drawn Tube, Rod & Bar Sheet & Plate, Rod & Bar Drawn Tube Extrusions Sheet & Plate Plate Sheet & Plate, Extrusions, Drawn Tube Sheet Sheet & Plate, Extrusions Sheet & Plate Plate
5050 All
5052 All 5052 All
5083 All 5083 All 5083 All
5086 All
5154 All
5454 All
5456 All 5456 All
All Extrusions Extrusions Extrusions Extrusions Extrusions Extrusions
6063 T5, T52, T6
6082 T6, T6511
6105 T5
6351 T5, T61 6351 T5, T62
6463 T6
7005 T53
8.7
16.8 12.2
14.5 14.5
21.6 19.2
13.3
12.2
15.7
18.0 20.4 19.2
10.4 11.0
6.5
5.4
7.0
9.3 9.3 8.7
5.4 4.8
3.7 3.2
Bc ksi
up thru 0.750
up thru 0.500
over 0.375
up thru 0.500
27.7
8.7
16.8 12.2
14.5
0.200 to 6.000 18.0
over 0.375
up thru 1.000 up thru 1.000
0.188-1.500 1.501-3.000
0.188 to 1.500 1.501 to 3.000
Thickness in.
Cc
Dp ksi
Cp
6.1 0.018 221 5.5 0.016 234
4.2 0.010 267 3.6 0.008 290
Bp ksi
Dt ksi
6.2 5.6
7.4 0.025 201
6.1 0.018 221
8.1 0.028 192
7.5
6.2 0.183
17.0 0.086 133 16.8 0.536 17.0 0.086 133 16.8 0.536
0.716 17.0 0.086 133 16.8 0.536
21.3 0.120 119 20.8
0.174 106 33.1 0.228 97 31.8
1.245
0.031 185 10.1 0.039 172 10.1 0.273
0.084 133 19.9 0.108 123 19.5 0.654 0.052 157 14.2 0.065 145 14.1 0.425
0.067 144
0.093 129
0.031 185 10.1 0.039 172 10.1 0.273
0.084 133 19.9 0.108 123 19.5 0.654 0.052 157 14.2 0.065 145 14.1 0.425
0.067 144 0.067 144
0.121 119 25.7 0.156 110 24.9 0.901 0.101 127 22.7 0.130 116 22.2 0.771
0.058 152 15.6 0.074 140 15.4 0.475
0.051 158 14.2 0.065 147 14.1 0.422
0.074 140 18.4 0.095 129 18.1 0.588
0.092 131 21.3 0.118 120 20.8 0.709 0.111 123 24.2 0.143 113 23.5 0.835 0.101 127 22.7 0.130 116 22.2 0.771
Cbr
8.1 0.028 192 7.2 0.024 203
9.8 0.038 174
112
1.385
115 25.1 115 25.1
1.261 1.261
115 25.1
31.2
1.261
1.684
15.1 0.642
257 44.1 0.350
84
715 13.4 0.060 150
47.7 2.929
15.1 0.642
390 26.4 0.165 106 29.2 1.539 524 18.9 0.100 126 21.1 0.999
446 22.6 0.131
366 28.3 0.184 103
715 13.4 0.060 150
390 26.4 0.165 106 29.2 1.539 524 18.9 0.100 126 21.1 0.999
446 22.6 0.131 446 22.6 0.131
499 34.1 0.240 95 37.4 2.120 532 30.2 0.200 101 33.3 1.815
1.117
21.1 0.993
27.1
1.668 1.966 1.815
18.1 0.812 19.1 0.872
11.2 0.431
9.3 0.335
12.2 0.481
16.1 0.698 16.1 0.698 15.1 0.642
9.3 0.335 8.3 0.289
495 20.7 0.113 122 23.1
680 18.9 0.099 127
427 24.5 0.146
Dtb ksi
6.4 0.204 5.5 0.165
Btb ksi
551 28.3 0.181 104 31.2 336 32.2 0.219 98 35.3 532 30.2 0.200 101 33.3
608 16.1 0.078 137 580 17.0 0.085 133
932
8.1 0.028 192
875 10.7 0.043 167
0.142 1066
8.1 0.204
Dbr ksi
5.5 0.016 232 4.7 0.012 252
Bbr ksi
672 14.3 0.066 145 672 14.3 0.066 145 715 13.4 0.060 150
0.142 1066 0.123 1150
0.041 170 12.1 0.051 158 12.1 0.345 0.044 166 12.8 0.056 153 12.7 0.371
0.020 215
0.015 236
0.023 206
Ct
4.3 0.087 1375 3.6 0.070 1540
Bt ksi
0.034 180 10.8 0.043 167 10.8 0.297 0.034 180 10.8 0.043 167 10.8 0.297 0.031 185 10.1 0.039 172 10.1 0.273
0.015 236 0.013 250
0.009 284 0.007 308
Dc ksi
1. When welded with 5183, 5356, or 5556 alloy filler regardless of thickness, and when welded with 4043, 5554, or 5654 alloy filler for thickness ≤ 0.375 in. 2. When welded with 4043, 5554, or 5654 alloy filler for thickness > 0.375 in.
All All
6061 T6, T651, T6510, T65111 6061 T6, T651, T6510, T65112
Extrusions Extrusions
Sheet & Plate
6005 T5 6005A T61
Sheet
Sheet & Plate Drawn Tube Sheet
3004 All 3004 All Alclad 3004 All
5005 All
Sheet & Plate, Drawn Tube Sheet & Plate, Drawn Tube
3003 All Alclad 3003 All
3005 All
Sheet & Plate, Drawn Tube Rod & Bar
Product
1100 All 1100 All
Alloy Temper
Table 1-2 BUCKLING CONSTANTS (WELDED) Ds ksi
0.013
0.012 7.3 0.024 7.8 0.026
4.5
3.7 0.009
4.9
6.5 0.020 6.5 0.020 6.1 0.018
3.7 0.009 3.3 0.007
2.5 0.005 2.2 0.004
Bs ksi
9.4 0.035
8.6 0.030
11.1 0.045
6.1
0.018
6.1 89 20.0
187
0.107
0.018
121 12.0 0.051 150 8.6 0.031
133 10.3 0.040
115 12.9 0.056
187
121 12.0 0.051 150 8.6 0.031
133 10.3 0.040 133 10.3 0.040
104 15.5 0.073 113 14.6 0.067
144
152
129
118 12.9 0.056 108 14.6 0.067 113 13.8 0.061
167 161
228
259
216
179 179 187
259 279
332 369
Ctb
125
221
158 187
171
152
221
158 187
171 171
141 145
181
188
166
155 145 150
203 197
258
285
247
214 214 221
285 301
344 373
Cs
Allowable Stresses for Building-Type Structures Tables 2-1 through 2-24 and 2-1W through 2-24W 1. These tables provide allowable stresses F/ for building-type structures determined in accordance with the Specification for Aluminum Structures. 2. Buckling constants used to calculate values in these tables are calculated from mechanical properties given in Part I Tables A.3.4 and A.3.5 rather than the rounded buckling constants given in Part VI Tables 1-1 and 1-2. 3. For tubes with circumferential welds, equations apply for Rb/t < 20.
January 2010
VI-9
Table 2-1 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
1100 – H14
D.2b
8.2
D.2a
8.5
Fty = 14 k/in Fcy = 13 k/in2 Ftu = 16 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
8.2 11.0 9.9 11.0
J.3.7a, J.4.7 J.3.7b, J.7
16.4 10.9 Slenderness S
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 10.2 see also F.4.2 9.2 see also F.6.2 10.2
S2
kL/r
7.5 – 0.035 S
144
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
8.8 – 0.034 S
172
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
F.4.2
(d/t)(Lb/(Cbd))1/2
F.6.2
Rb/t
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-10
E = 10,100 k/in2 kt = 1
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Sheet, Plate, Drawn Tube 2
G.2
F/ for S ≤ S1
S1
8.8 – 0.065 S1/2 8072 13.7 – 0.182 S 15.2 - 0.764 S1/2 133
10.2 – 0.325 S1/2
50 446
F/ for S ≥ S2
23,599 /S 11,420 /S2 3,776 /[S(1+S1/2/35)2]
b/t
7.9
9.4 10.3 – 0.259 S
27
b/t
7.9
9.4 10.3 – 0.259 S
19.9 103 /S
b/t
7.9
29.4 10.3 – 0.083 S
ls
7.9
22.1
Rb/t
7.9
49.0 10.2 – 0.325 S1/2
leq
7.9
47.0 10.3 – 0.052 S
99
513 /S
b/t
10.2
66.9 13.7 – 0.052 S
133
909 /S
b/t
10.2
12.4 13.7 – 0.278 S
33
4,932 /S2
b/t
10.2
150.0 13.7 – 0.023 S
298
2,037 /S
leq
10.2
43.5 13.7 – 0.079 S
86
b/t
5.1
48.5
8.8 – 0.041 S
6.8 – 0.034 S
62
2,417 /S2
320 /S
144
60,414 /S2
446
3,776 /[S(1+S1/2/35)2]
131
591 /S
38,665 /S2
January 2010
Table 2-2 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
3003 – H14
Sheet, Plate, Drawn Tube
D.2b
10.3
E = 10,100 k/in2 kt = 1
D.2a
10.3
Fty = 17 k/in Fcy = 14 k/in2 Ftu = 20 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
10.3 13.4 12.1 13.4
J.3.7a, J.4.7 J.3.7b, J.7
20.5 13.6 Slenderness S
S2
kL/r
8.1 – 0.039 S
138
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
9.5 – 0.038 S
166
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
F.4.2
(d/t)(Lb/(Cbd))1/2
F.6.2
Rb/t
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 11.0 see also F.4.2 9.9 see also F.6.2 11.0
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
F/ for S ≤ S1
S1
9.5 – 0.073 S1/2 7466 14.8 – 0.206 S 16.5 – 0.847 S1/2 127
11.0 – 0.360 S1/2
48 416
F/ for S ≥ S2
23,599 /S 11,420 /S2 3,776 /[S(1+S1/2/35)2]
b/t
8.5
9.2 11.2 – 0.292 S
25
2,417 /S2
b/t
8.5
9.2 11.2 – 0.292 S
19.1
107 /S
b/t
8.5
28.7 11.2 – 0.094 S
60
333 /S
ls
8.5
21.9
Rb/t
8.5
47.6 11.0 – 0.360 S1/2
leq
8.5
46.0 11.2 – 0.058 S
96
534 /S
b/t
11.0
65.5 14.8 – 0.058 S
128
946 /S
b/t
11.0
12.2 14.8 – 0.313 S
32
4,932 /S2
b/t
11.0
146.8 14.8 – 0.026 S
286
2,120 /S
leq
11.0
42.6 14.8 – 0.089 S
83
b/t
6.2
45.8
9.5 – 0.046 S
8.3 – 0.047 S
138
60,414 /S2
416
3,776 /[S(1+S1/2/35)2]
118
615 /S
38,665 /S2
VI-11
Table 2-3 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
3003 – H16
Sheet
D.2b
12.3
Fty = 21 k/in Fcy = 18 k/in2 Ftu = 24 k/in2
E = 10,100 k/in2 kt = 1
D.2a
12.7
2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
12.3 16.5 14.9 16.5
J.3.7a, J.4.7 J.3.7b, J.7
24.6 16.4 Slenderness S
E.3
F/ for S ≤ S1
S1
kL/r
F/ for S1 < S < S2
S2
10.5 – 0.058 S
121
51,352 /S2
145
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
12.4 – 0.109 S1/2 5726
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
19.5 – 0.310 S
11,420 /S2
F.6.2
Rb/t
G.2
12.4 – 0.057 S
F/ for S ≥ S2
Lb/(ryeCb1/2)
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-12
see B.5.4.1 thru B.5.4.5 and E.4.2 14.2 see also F.4.2 12.8 see also F.6.2 14.2
F.2.1
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
21.4 – 1.203 S1/2 106
14.3 – 0.511 S1/2
42 327
3,776 /[S(1+S1/2/35)2]
b/t
10.9
8.5 14.7 – 0.440 S
22
b/t
10.9
8.5 14.7 – 0.440 S
16.7 122 /S
b/t
10.9
26.7 14.7 – 0.141 S
52
ls
10.9
21.5 12.4 – 0.068 S
121
60,414 /S2
Rb/t
10.9
43.2 14.3 – 0.511 S1/2
327
3,776 /[S(1+S1/2/35)2]
leq
10.9
42.7 14.7 – 0.088 S
b/t
14.2
60.7
19.5 – 0.088 S
111
1,085 /S
b/t
14.2
11.3
19.5 – 0.472 S
28
4,932 /S2
b/t
14.2
136.2 19.5 – 0.039 S
249
2,431 /S
leq
14.2
39.5
19.5 – 0.135 S
72
b/t
7.6
43.0
10.5 – 0.067 S
105
83
2,417 /S2
382 /S
611 /S
705 /S
38,665 /S2
January 2010
Table 2-4 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
Alclad 3004 – H34
D.2b
15.9
D.2a
14.5
Fty = 24 k/in Fcy = 21 k/in2 Ftu = 31 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
14.5 18.9 17.0 18.9
J.3.7a, J.4.7 J.3.7b, J.7
31.8 21.1 Slenderness S
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 16.5 see also F.4.2 14.9 see also F.6.2 16.5
S2
kL/r
12.4 – 0.074 S
112
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
14.6 – 0.073 S
134
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
14.6 – 0.139 S1/2 4862
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
23.1 – 0.399 S
11,420 /S2
F.6.2
Rb/t
25.2 – 1.492 S1/2
b/t
12.7
8.2
17.3 – 0.565 S
20
b/t
12.7
8.2
17.3 – 0.565 S
15.3 133 /S
b/t
12.7
25.5
17.3 – 0.181 S
48
ls
12.7
21.2 14.6 – 0.087 S
112
60,414 /S2
Rb/t
12.7
40.6 16.8 – 0.634 S1/2
282
3,776 /[S(1+S1/2/35)2]
leq
12.7
40.8
17.3 – 0.113 S
77
b/t
16.5
57.9 23.1 – 0.113 S
102
1,180 /S
b/t
16.5
10.8 23.1 – 0.608 S
25
4,932 /S2
b/t
16.5
129.9 23.1 – 0.050 S
229
2,644 /S
leq
16.5
37.7 23.1 – 0.174 S
66
767 /S
b/t
8.7
41.3 12.1 – 0.083 S
98
38,665 /S2
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
E = 10,100 k/in2 kt = 1
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on one B.5.4.1 edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Sheet
G.2
F/ for S ≤ S1
S1
95
16.8 – 0.634 S1/2
39 282
F/ for S ≥ S2
3,776 /[S(1+S1/2/35)2] 2,417 /S2
415 /S
665 /S
VI-13
Table 2-5 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5005 – H14
Sheet and Plate
D.2b
10.8
E = 10,100 k/in2 kt = 1
D.2a
10.3
Fty = 17 k/in Fcy = 15 k/in2 Ftu = 21 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
10.3 13.4 12.1 13.4
J.3.7a, J.4.7 J.3.7b, J.7
21.5 14.3 Slenderness S
S2
kL/r
8.7 – 0.043 S
133
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
10.2 – 0.043 S
160
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
10.2 – 0.082 S1/2 6943
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
16.0 – 0.230 S
11,420 /S2
F.6.2
Rb/t
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-14
see B.5.4.1 thru B.5.4.5 and E.4.2 11.8 see also F.4.2 10.6 see also F.6.2 11.8
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
F/ for S ≤ S1
17.7 – 0.933 S1/2
S1
121
11.8 – 0.396 S1/2
46 390
F/ for S ≥ S2
3,776 /[S(1+S1/2/35)2]
b/t
9.1
9.0
12.0 – 0.327 S
25
2,417 /S2
b/t
9.1
9.0
12.0 – 0.327 S
18.4 111 /S
b/t
9.1
28.2
12.0 – 0.105 S
58
ls
9.1
21.8
10.2 – 0.051 S
133
60,414 /S2
Rb/t
9.1
46.4
11.8 – 0.396 S1/2
390
3,776 /[S(1+S1/2/35)2]
leq
9.1
45.1
12.0 – 0.065 S
92
554 /S
b/t
11.8
64.2
16.0 – 0.065 S
123
982 /S
b/t
11.8
11.9
16.0 – 0.350 S
30
4,932 /S2
b/t
11.8
143.8 16.0 – 0.029 S
275
2,201 /S
leq
11.8
41.7
16.0 – 0.100 S
80
b/t
6.2
45.8
8.3 – 0.047 S
118
346 /S
638 /S
38,665 /S2
January 2010
Table 2-6 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5005 – H32
Sheet and Plate
D.2b
8.7
E = 10,100 k/in2 kt = 1
D.2a
7.3
Fty = 12 k/in Fcy = 11 k/in2 Ftu = 17 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
7.3 9.5 8.5 9.5
J.3.7a, J.4.7 J.3.7b, J.7
17.4 11.6 Slenderness S
S2
kL/r
6.3 – 0.027 S
157
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
7.4 – 0.026 S
188
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
F.4.2
(d/t)(Lb/(Cbd))1/2
F.6.2
Rb/t
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 8.7 see also F.4.2 7.8 see also F.6.2 8.7
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
F/ for S ≤ S1
S1
7.4 – 0.050 S1/2 9618 11.4 – 0.139 S 12.8 – 0.606 S1/2 150
8.5 – 0.257 S1/2
55 524
F/ for S ≥ S2
23,599 /S 11,420 /S2 3,776 /[S(1+S1/2/35)2]
b/t
6.7
9.8
8.6 – 0.198 S
29
2,417 /S2
b/t
6.7
9.8
8.6 – 0.198 S
21.8 94 /S
b/t
6.7
30.8
8.6 – 0.063 S
68
ls
6.7
22.3
7.4 – 0.031 S
157
60,414 /S2
Rb/t
6.7
52.2
8.5 – 0.257 S1/2
524
3,776 /[S(1+S1/2/35)2]
leq
6.7
49.2
8.6 – 0.040 S
109
468 /S
b/t
8.7
70.3
11.4 – 0.039 S
145
830 /S
b/t
8.7
13.0
11.4 – 0.212 S
36
4,932 /S2
b/t
8.7
157.5
11.4 – 0.018 S
326
1,861 /S
leq
8.7
45.7
11.4 – 0.060 S
94
b/t
4.4
50.7
5.7 – 0.027 S
142
293 /S
540 /S
38,665 /S2
VI-15
Table 2-7 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5005 – H34
Sheet and Plate
D.2b
10.3
E = 10,100 k/in2 kt = 1
D.2a
9.1
Fty = 15 k/in Fcy = 14 k/in2 Ftu = 20 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
9.1 11.8 10.6 11.8
J.3.7a, J.4.7 J.3.7b, J.7
20.5 13.6 Slenderness S
S2
kL/r
8.1 – 0.039 S
138
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
9.5 – 0.038 S
166
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
F.4.2
(d/t)(Lb/(Cbd))1/2
F.6.2
Rb/t
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-16
see B.5.4.1 thru B.5.4.5 and E.4.2 11.0 see also F.4.2 9.9 see also F.6.2 11.0
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
F/ for S ≤ S1
S1
9.5 – 0.073 S1/2 7466
23,599 /S
48
11,420 /S2
14.8 – 0.206 S 16.5 – 0.847 S1/2 127
F/ for S ≥ S2
11.0 – 0.360 S1/2
416
3,776 /[S(1+S1/2/35)2]
b/t
8.5
9.2
11.2 – 0.292 S
25
b/t
8.5
9.2
11.2 – 0.292 S
19.1 107 /S
b/t
8.5
28.7
11.2 – 0.094 S
60
ls
8.5
21.9
9.5 – 0.046 S
138
60,414 /S2
Rb/t
8.5
47.6
11.0 – 0.360 S1/2
416
3,776 /[S(1+S1/2/35)2]
leq
8.5
46.0
11.2 – 0.058 S
96
534 /S
b/t
11.0
65.5 14.8 – 0.058 S
128
946 /S
b/t
11.0
12.2 14.8 – 0.313 S
32
4,932 /S2
b/t
11.0
146.8 14.8 – 0.026 S
286
2,120 /S
leq
11.0
42.6 14.8 – 0.089 S
83
b/t
5.5
47.5
7.3 – 0.038 S
126
2,417 /S2
333 /S
615 /S
38,665 /S2
January 2010
Table 2-8 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5050 – H34
Sheet
D.2b
12.8
E = 10,100 k/in2 kt = 1
D.2a
12.1
Fty = 20 k/in Fcy = 18 k/in2 Ftu = 25 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
12.1 15.8 14.2 15.8
J.3.7a, J.4.7 J.3.7b, J.7
25.6 17.1 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
10.5 – 0.058 S
F.2.1
Lb/(ryeCb1/2)
12.4 – 0.057 S
F.3.1
2LbSc/(Cb(IyJ)1/2)
12.4 – 0.109 S1/2 5726
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
19.5 – 0.310 S
11,420 /S2
F.6.2
Rb/t
21.4 – 1.203 S1/2
b/t
10.9
8.5 14.7 – 0.440 S
22
b/t
10.9
8.5 14.7 – 0.440 S
16.7 122 /S
b/t
10.9
26.7 14.7 – 0.141 S
52
ls
10.9
21.5 12.4 – 0.068 S
121
60,414 /S2
Rb/t
10.9
43.2 14.3 – 0.511 S1/2
327
3,776 /[S(1+S1/2/35)2]
leq
10.9
42.7 14.7 – 0.088 S
83
b/t
14.2
60.7 19.5 – 0.088 S
111
1,085 /S
b/t
14.2
11.3 19.5 – 0.472 S
28
4,932 /S2
b/t
14.2
136.2 19.5 – 0.039 S
249
2,431 /S
leq
14.2
39.5 19.5 – 0.135 S
72
b/t
7.3
43.6 10.0 – 0.061 S
108
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 14.2 see also F.4.2 12.8 see also F.6.2 14.2
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
106
14.3 – 0.511 S1/2
121 145
42 327
51,352 /S2 86,996 /S2
3,776 /[S(1+S1/2/35)2] 2,417 /S2
382 /S
611 /S
705 /S
38,665 /S2
VI-17
Table 2-9 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5052 – H32
Sheet, Plate, Drawn Tube
D.2b
15.9
E = 10,200 k/in2 kt = 1
D.2a
13.9
Fty = 23 k/in Fcy = 21 k/in2 Ftu = 31 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
13.9 18.1 16.3 18.1
J.3.7a, J.4.7 J.3.7b, J.7
31.8 21.1 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2 12.4 – 0.074 S
F.2.1
Lb/(ryeCb1/2)
14.6 – 0.072 S
F.3.1
F/ for S ≥ S2
S2 112
51,860 /S2
135
87,857 /S2
2LbSc/(Cb(IyJ)1/2)
14.6 – 0.139 S1/2 4910
23,833 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
23.1 – 0.397 S
11,533 /S2
F.6.2
Rb/t
25.2 – 1.487 S1/2
b/t
12.7
8.2
17.3 – 0.563 S
21
b/t
12.7
8.2
17.3 – 0.563 S
15.4 134 /S
b/t
12.7
25.6
17.3 – 0.180 S
48
ls
12.7
21.3 14.6 – 0.087 S
112
61,012 /S2
Rb/t
12.7
40.9 16.8 – 0.632 S1/2
285
3,813 /[S(1+S1/2/35)2]
leq
12.7
41.0
17.3 – 0.113 S
77
b/t
16.5
58.2 23.1 – 0.112 S
103
1,186 /S
b/t
16.5
10.8 23.1 – 0.605 S
25
4,981 /S2
b/t
16.5
130.5 23.1 – 0.050 S
230
2,657 /S
leq
16.5
37.9 23.1 – 0.173 S
67
b/t
8.4
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-18
see B.5.4.1 thru B.5.4.5 and E.4.2 16.5 see also F.4.2 14.9 see also F.6.2 16.5
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
96
42.0
16.8 – 0.632 S1/2
11.6 – 0.077 S
39 285
101
3,813 /[S(1+S1/2/35)2] 2,440 /S2
417 /S
668 /S
771 /S
39,048 /S2
January 2010
Table 2-10 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5052 – H34
Sheet, Plate, Drawn Tube
D.2b
17.4
E = 10,200 k/in2 kt = 1
D.2a
15.8
Fty = 26 k/in Fcy = 24 k/in2 Ftu = 34 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
15.8 20.5 18.4 20.5
J.3.7a, J.4.7 J.3.7b, J.7
34.9 23.2 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
14.3 – 0.091 S
104
51,860 /S2
F.2.1
Lb/(ryeCb1/2)
16.8 – 0.089 S
125
87,857 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
16.8 – 0.172 S1/2 4259
23,833 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
26.7 – 0.495 S
11,533 /S2
F.6.2
Rb/t
28.9 – 1.793 S1/2
b/t
14.5
7.9 20.1 – 0.700 S
19
b/t
14.5
7.9 20.1 – 0.700 S
14.3 144 /S
b/t
14.5
24.6 20.1 – 0.224 S
45
ls
14.5
21.0 16.8 – 0.107 S
104
61,012 /S2
Rb/t
14.5
38.8 19.3 – 0.762 S1/2
250
3,813 /[S(1+S1/2/35)2]
leq
14.5
39.4 20.1 – 0.140 S
72
718 /S
b/t
18.9
55.9 26.7 – 0.140 S
96
1,276 /S
b/t
18.9
10.4 26.7 – 0.753 S
24
4,981 /S2
b/t
18.9
125.2 26.7 – 0.062 S
214
2,859 /S
leq
18.9
36.3 26.7 – 0.215 S
62
829 /S
b/t
9.5
40.5 13.3 – 0.094 S
94
39,048 /S2
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 18.9 see also F.4.2 17.0 see also F.6.2 18.9
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
88
19.3 – 0.762 S1/2
36 250
3,813 /[S(1+S1/2/35)2] 2,440 /S2
449 /S
VI-19
Table 2-11 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5052 – H36
Sheet
D.2b
19.0
E = 10,200 k/in2 kt = 1
D.2a
17.6
Fty = 29 k/in Fcy = 26 k/in2 Ftu = 37 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
17.6 22.8 20.6 22.8
J.3.7a, J.4.7 J.3.7b, J.7
37.9 25.2 Slenderness S
E.3
F/ for S ≤ S1
S1
kL/r
F/ for S1 < S < S2
S2
15.6 – 0.104 S
100
51,860 /S2
120
87,857 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
18.3 – 0.195 S1/2 3910
23,833 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
29.2 – 0.565 S
11,533 /S2
F.6.2
Rb/t
31.5 – 2.005 S1/2
b/t
15.8
7.7 21.9 – 0.798 S
18
b/t
15.8
7.7 21.9 – 0.798 S
13.7 150 /S
b/t
15.8
24.0 21.9 – 0.255 S
43
ls
15.8
20.8 18.3 – 0.122 S
100
61,012 /S2
Rb/t
15.8
37.6 21.0 – 0.852 S1/2
231
3,813 /[S(1+S1/2/35)2]
leq
15.8
38.5 21.9 – 0.160 S
69
751 /S
b/t
20.5
54.5 29.2 – 0.160 S
91
1,333 /S
b/t
20.5
10.1 29.2 – 0.859 S
23
4,981 /S2
b/t
20.5
122.1 29.2 – 0.071 S
205
2,988 /S
leq
20.5
35.4 29.2 – 0.246 S
59
866 /S
b/t
10.5
39.1 14.9 – 0.112 S
89
39,048 /S2
G.2
18.3 – 0.102 S
F/ for S ≥ S2
Lb/(ryeCb1/2)
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-20
see B.5.4.1 thru B.5.4.5 and E.4.2 20.5 see also F.4.2 18.4 see also F.6.2 20.5
F.2.1
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
83
21.0 – 0.852 S1/2
34 231
3,813 /[S(1+S1/2/35)2] 2,440 /S2
469 /S
January 2010
Table 2-12 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5083 – H116, H32, H321
heet and Plate S (0.188 to 1.500 in. thick)
D.2b
22.6
D.2a
18.8
Fty = 31 k/in2 Fcy = 26 k/in2 Ftu = 44 k/in2
E = 10,400 k/in2 kt = 1
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
18.8 24.4 22.0 24.4
J.3.7a, J.4.7 J.3.7b, J.7
45.1 30.0 Slenderness S
E.3
F/ for S ≤ S1
S1
kL/r
F/ for S1 < S < S2
S2
15.6 – 0.103 S
101
52,877 /S2
121
89,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
18.3 – 0.193 S1/2 3987
24,300 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
29.2 – 0.559 S
11,760 /S2
F.6.2
Rb/t
31.5 – 1.992 S1/2
b/t
15.8
7.8 21.9 – 0.790 S
18
b/t
15.8
7.8 21.9 – 0.790 S
13.9 152 /S
b/t
15.8
24.3 21.9 – 0.253 S
43
ls
15.8
21.0 18.3 – 0.121 S
101
62,208 /S2
Rb/t
15.8
38.1 21.0 – 0.847 S1/2
235
3,888 /[S(1+S1/2/35)2]
leq
15.8
38.8 21.9 – 0.158 S
69
758 /S
b/t
20.5
55.0 29.2 – 0.158 S
92
1,346 /S
b/t
20.5
10.2 29.2 – 0.851 S
23
5,078 /S2
b/t
20.5
123.3 29.2 – 0.071 S
207
3,017 /S
leq
20.5
35.8 29.2 – 0.243 S
60
875 /S
b/t
11.3
38.7 16.1 – 0.124 S
86
39,813 /S2
G.2
18.3 – 0.101 S
F/ for S ≥ S2
Lb/(ryeCb1/2)
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 20.5 see also F.4.2 18.4 see also F.6.2 20.5
F.2.1
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
84
21.0 – 0.847 S1/2
35 235
3,888 /[S(1+S1/2/35)2] 2,488 /S2
474 /S
VI-21
Table 2-13 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5086 – H34
Sheet, Plate, Drawn Tube
D.2b
22.6
E = 10,400 k/in2 kt = 1
D.2a
20.6
Fty = 34 k/in Fcy = 32 k/in2 Ftu = 44 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
20.6 26.8 24.1 26.8
J.3.7a, J.4.7 J.3.7b, J.7
45.1 30.0 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
19.4 – 0.143 S
90
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
22.9 – 0.141 S
108
89,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
22.9 – 0.270 S1/2 3191
24,300 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
36.7 – 0.788 S
11,760 /S2
F.6.2
Rb/t
31.5 – 2.665 S1/2
b/t
19.4
7.3
27.5 – 1.112 S
16
b/t
19.4
7.3
27.5 – 1.112 S
12.4 170 /S
b/t
19.4
22.8
27.5 – 0.356 S
39
531 /S
ls
19.4
20.6 22.9 – 0.169 S
90
62,208 /S2
Rb/t
19.4
35.0 26.1 – 1.132 S1/2
leq
19.4
36.4
27.5 – 0.222 S
62
849 /S
b/t
25.2
51.5 36.7 – 0.223 S
82
1,509 /S
b/t
25.2
9.6 36.7 – 1.199 S
20
5,078 /S2
b/t
25.2
115.4 36.7 – 0.099 S
185
3,382 /S
leq
25.2
33.5 36.7 – 0.343 S
54
981 /S
b/t
12.4
37.5
82
39,813 /S2
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-22
see B.5.4.1 thru B.5.4.5 and E.4.2 25.2 see also F.4.2 22.7 see also F.6.2 25.2
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
73
26.1 – 1.132 S1/2
17.8 – 0.145 S
31 192
192
3,888 /[S(1+S1/2/35)2] 2,488 /S2
3,888 /[S(1+S1/2/35)2]
January 2010
Table 2-14 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5086 – H116 5086 – H32
Sheet and Plate Drawn Tube, Sheet and Plate
D.2b
20.5
D.2a
17.0
Fty = 28 k/in2 Fcy = 26 k/in2 Ftu = 40 k/in2
E = 10,400 k/in2 kt = 1
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
17.0 22.1 19.9 22.1
J.3.7a, J.4.7 J.3.7b, J.7
41.0 27.3 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
15.6 – 0.103 S
101
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
18.3 – 0.101 S
121
89,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
18.3 – 0.193 S1/2 3987
24,300 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
29.2 – 0.559 S
11,760 /S2
F.6.2
Rb/t
31.5 – 1.992 S1/2
b/t
15.8
7.8 21.9 – 0.790 S
18
b/t
15.8
7.8 21.9 – 0.790 S
13.9 152 /S
b/t
15.8
24.3 21.9 – 0.253 S
43
ls
15.8
21.0 18.3 – 0.121 S
101
62,208 /S2
Rb/t
15.8
38.1 21.0 – 0.847 S1/2
235
3,888 /[S(1+S1/2/35)2]
leq
15.8
38.8 21.9 – 0.158 S
69
758 /S
b/t
20.5
55.0 29.2 – 0.158 S
92
1,346 /S
b/t
20.5
10.2 29.2 – 0.851 S
23
5,078 /S2
b/t
20.5
123.3 29.2 – 0.071 S
207
3,017 /S
leq
20.5
35.8 29.2 – 0.243 S
60
875 /S
b/t
10.2
39.9 14.4 – 0.105 S
91
39,813 /S2
Elements—Flexural Compression flat elements supported on both B.5.5.1 edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 20.5 see also F.4.2 18.4 see also F.6.2 20.5
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported B.5.4.2 on both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
84
21.0 – 0.847 S1/2
35 235
3,888 /[S(1+S1/2/35)2] 2,488 /S2
474 /S
VI-23
Table 2-15 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5454 – H32
Sheet and Plate
D.2b
18.5
E = 10,400 k/in2 kt = 1
D.2a
15.8
Fty = 26 k/in Fcy = 24 k/in2 Ftu = 36 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
15.8 20.5 18.4 20.5
J.3.7a, J.4.7 J.3.7b, J.7
36.9 24.6 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
14.3 – 0.090 S
105
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
16.8 – 0.089 S
127
89,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
16.8 – 0.170 S1/2 4343
24,300 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
26.7 – 0.490 S
11,760 /S2
F.6.2
Rb/t
28.9 – 1.781 S1/2
b/t
14.5
8.0 20.1 – 0.693 S
19
b/t
14.5
8.0 20.1 – 0.693 S
14.5 145 /S
b/t
14.5
24.9 20.1 – 0.222 S
45
ls
14.5
21.2 16.8 – 0.106 S
105
62,208 /S2
Rb/t
14.5
39.3 19.3 – 0.757 S1/2
255
3,888 /[S(1+S1/2/35)2]
leq
14.5
39.8 20.1 – 0.139 S
72
725 /S
b/t
18.9
56.4 26.7 – 0.139 S
96
1,288 /S
b/t
18.9
10.5 26.7 – 0.746 S
24
5,078 /S2
b/t
18.9
126.4 26.7 – 0.062 S
216
2,887 /S
leq
18.9
36.7 26.7 – 0.213 S
63
837 /S
b/t
9.5
40.8 13.3 – 0.093 S
95
39,813 /S2
Elements—Flexural Compression flat elements supported on both B.5.5.1 edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-24
see B.5.4.1 thru B.5.4.5 and E.4.2 18.9 see also F.4.2 17.0 see also F.6.2 18.9
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported B.5.4.2 on both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
89
19.3 – 0.757 S1/2
36 255
3,888 /[S(1+S1/2/35)2] 2,488 /S2
453 /S
January 2010
Table 2-16 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5454 – H34
Sheet and Plate
D.2b
20.0
E = 10,400 k/in2 kt = 1
D.2a
17.6
Fty = 29 k/in Fcy = 27 k/in2 Ftu = 39 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
17.6 22.8 20.6 22.8
J.3.7a, J.4.7 J.3.7b, J.7
40.6 26.6 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
16.2 – 0.109 S
99
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
19.1 – 0.107 S
119
89,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
19.1 – 0.205 S1/2 3829
24,300 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
30.4 – 0.595 S
11,760 /S2
F.6.2
Rb/t
32.7 – 2.100 S1/2
b/t
16.4
7.7 22.8 – 0.841 S
18
b/t
16.4
7.7 22.8 – 0.841 S
13.6 155 /S
b/t
16.4
24.0 22.8 – 0.269 S
42
484 /S
ls
16.4
21.0 19.1 – 0.128 S
99
62,208 /S2
Rb/t
16.4
37.5 21.8 – 0.893 S1/2
leq
16.4
38.4 22.8 – 0.168 S
68
774 /S
b/t
21.3
54.4 30.4 – 0.168 S
90
1,374 /S
b/t
21.3
10.1 30.4 – 0.906 S
22
5,078 /S2
b/t
21.3
121.8 30.4 – 0.075 S
203
3,080 /S
leq
21.3
35.3 30.4 – 0.259 S
59
893 /S
b/t
10.5
39.5 14.9 – 0.111 S
89
39,813 /S2
Elements—Flexural Compression flat elements supported on both B.5.5.1 edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 21.3 see also F.4.2 19.1 see also F.6.2 21.3
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported B.5.4.2 on both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
82
21.8 – 0.893 S1/2
34 227
227
3,888 /[S(1+S1/2/35)2] 2,488 /S2
3,888 /[S(1+S1/2/35)2]
VI-25
Table 2-17 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
D.2b
19.5
D.2a
21.2 Tension
F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
19.5 27.6 24.2 27.6
J.3.7a, J.4.7 J.3.7b, J.7
39.0 25.9 Slenderness S
E.3
E = 10,100 k/in2 kt = 1
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 27.6 see also F.4.2 24.8 see also F.6.2 27.6
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
20.3 – 0.127 S
66
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
23.9 – 0.124 S
79
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
23.9 – 0.238 S1/2 1685
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
40.5 – 0.928 S
11,420 /S2
F.6.2
Rb/t
39.3 – 2.702 S1/2
b/t
21.2
6.7
27.3 – 0.910 S
12
2,417 /S2
b/t
21.2
6.7
27.3 – 0.910 S
10.5
186 /S
b/t
21.2
20.8
27.3 – 0.291 S
33
580 /S
ls
21.2
17.8
23.9 – 0.149 S
66
60,414 /S2
Rb/t
21.2
27.6
26.2 – 0.944 S1/2
leq
21.2
33.3
27.3 – 0.182 S
52
928 /S
b/t
27.6
49.3
40.5 - 0.262 S
77
1,563 /S
b/t
27.6
9.2
40.5 - 1.412 S
19
4,932 /S2
b/t
27.6
110.5
40.5 - 0.117 S
173
3,502 /S
leq
27.6
32.0
40.5 - 0.403 S
50
1,016 /S
35.3
16.5 - 0.107 S
63
38,665 /S2
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-26
Fty = 35 k/in2 Fcy = 35 k/in2 Ftu = 38 k/in2
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
6005A - T61 Extrusions (up through 1.000 in. thick)
G.2
b/t
12.7
55
26.2 – 0.944 S1/2
29 141
141
3,776 /[S(1+S1/2/35)2]
3,776 /[S(1+S1/2/35)2]
January 2010
Table 2-18 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
6061 - T6 6061 - T651
Sheet, Rod & Bar, Drawn Tube Plate (Up thru 4.000 in. thick)
D.2b
21.5
D.2a
21.2
Fty = 35 k/in2 Fcy = 35 k/in2 Ftu = 42 k/in2
E = 10,100 k/in2 kt = 1
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
21.2 27.6 24.8 27.6
J.3.7a, J.4.7 J.3.7b, J.7
43.1 28.6 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
20.3 – 0.127 S
66
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
23.9 – 0.124 S
79
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
23.9 – 0.238 S1/2
F.4.2
(d/t)(Lb/(Cbd))1/2
40.5 – 0.928 S
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 27.6 see also F.4.2 24.8 see also F.6.2 27.6
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
39.3 – 2.702 S1/2
55
26.2 – 0.944 S1/2
1685
23,599 /S
29
11,420 /S2
141
3,776 /[S(1+S1/2/35)2]
b/t
21.2
6.7 27.3 – 0.910 S
12
2,417 /S2
b/t
21.2
6.7 27.3 – 0.910 S
10.5
186 /S
b/t
21.2
20.8 27.3 – 0.291 S
33
580 /S
ls
21.2
17.8 23.9 – 0.149 S
66
60,414 /S2
Rb/t
21.2
27.6 26.2 – 0.944 S1/2
leq
21.2
33.3 27.3 – 0.182 S
52
928 /S
b/t
27.6
49.3
40.5 – 0.262 S
77
1,563 /S
b/t
27.6
9.2
40.5 – 1.412 S
19
4,932 /S2
b/t
27.6
110.5
40.5 – 0.117 S
173
3,502 /S
leq
27.6
32.0
40.5 – 0.403 S
50
1,016 /S
b/t
12.7
35.3
16.5 – 0.107 S
63
38,665 /S2
141
3,776 /[S(1+S1/2/35)2]
VI-27
Table 2-19 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateraltorsional buckling round tubes local buckling
Section
F/
D.2b
19.5
D.2a
21.2 Tension
F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
19.5 27.6 24.2 27.6
J.3.7a, J.4.7 J.3.7b, J.7
39.0 25.9 Slenderness S
E = 10,100 k/in2 kt = 1
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 27.6 see also F.4.2 24.8 see also F.6.2 27.6
S2
kL/r
20.3 – 0.127 S
66
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
23.9 – 0.124 S
79
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
23.9 – 0.238 S1/2
F.4.2
(d/t)(Lb/(Cbd))1/2
40.5 – 0.928 S
F.6.2
Rb/t
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-28
Fty = 35 k/in2 Fcy = 35 k/in2 Ftu = 38 k/in2
Extrusions Pipe Extrusions
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
6061 – T6, T6510, T6511 6061 – T6 6351 - T5
G.2
F/ for S ≤ S1
39.3 – 2.702 S1/2
S1
55
26.2 – 0.944 S1/2
F/ for S ≥ S2
1685
23,599 /S
29
11,420 /S2
141
3,776 /[S(1+S1/2/35)2]
b/t
21.2
6.7
27.3 – 0.910 S
12
2,417 /S2
b/t
21.2
6.7
27.3 – 0.910 S
10.5
186 /S
b/t
21.2
20.8
27.3 – 0.291 S
33
580 /S
ls
21.2
17.8 23.9 – 0.149 S
66
60,414 /S2
Rb/t
21.2
27.6 26.2 – 0.944 S1/2
leq
21.2
33.3
27.3 – 0.182 S
52
928 /S
b/t
27.6
49.3 40.5 – 0.262 S
77
1,563 /S
b/t
27.6
9.2 40.5 – 1.412 S
19
4,932 /S2
b/t
27.6
110.5 40.5 – 0.117 S
173
3,502 /S
leq
27.6
32.0 40.5 – 0.403 S
50
1,016 /S
b/t
12.7
35.3 16.5 – 0.107 S
63
38,665 /S2
141
3,776 /[S(1+S1/2/35)2]
January 2010
Table 2-20 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
6063 – T5 6063 – T52
Extrusions (Up thru 0.500 in. thick) Extrusions (Up thru 1.000 in. thick)
D.2b
11.3
D.2a
9.7
Fty = 16 k/in2 Fcy = 16 k/in2 Ftu = 22 k/in2
E = 10,100 k/in2 kt = 1
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
9.7 12.6 11.3 12.6
J.3.7a, J.4.7 J.3.7b, J.7
22.6 15.0 Slenderness S
E.3
F/ for S ≤ S1
S1
kL/r
F/ for S1 < S < S2
S2
8.9 – 0.037 S
99
51,352 /S2
10.5 – 0.036 S
119
86,996 /S2
3823
23,599 /S
45
11,420 /S2
Lb/(ryeCb1/2)
F.3.1
2LbSc/(Cb(IyJ)1/2)
10.5 – 0.070 S1/2
F.4.2
(d/t)(Lb/(Cbd))1/2
17.2 – 0.256 S
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 12.6 see also F.4.2 11.3 see also F.6.2 12.6
F.2.1
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
17.5 – 0.917 S1/2
95
11.6 – 0.320 S1/2
275
F/ for S ≥ S2
3,776 /[S(1+S1/2/35)2]
b/t
9.7
8.2
11.8 – 0.260 S
19
2,417 /S2
b/t
9.7
8.2
11.8 – 0.260 S
15.9
122 /S
b/t
9.7
25.6
11.8 – 0.083 S
50
382 /S
ls
9.7
18.8
10.5 – 0.044 S
99
60,414 /S2
Rb/t
9.7
36.7
11.6 – 0.320 S1/2
leq
9.7
41.0
11.8 – 0.052 S
80
b/t
12.6
62.9
17.2 – 0.072 S
119
1,017 /S
b/t
12.6
11.7
17.2 – 0.389 S
29
4,932 /S2
b/t
12.6
141.1
17.2 – 0.032 S
266
2,280 /S
leq
12.6
40.9
17.2 – 0.111 S
77
661 /S
b/t
5.8
43.6
7.2 – 0.031 S
96
38,665 /S2
275
3,776 /[S(1+S1/2/35)2] 611 /S
VI-29
Table 2-21 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Section Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
F/
6063 – T6
D.2b
15.4
D.2a
15.2
Fty = 25 k/in Fcy = 25 k/in2 Ftu = 30 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
15.2 19.7 17.7 19.7
J.3.7a, J.4.7 J.3.7b, J.7
30.8 20.5 Slenderness S
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 19.7 see also F.4.2 17.7 see also F.6.2 19.7
S2
kL/r
14.2 – 0.074 S
78
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
16.7 – 0.073 S
94
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
16.7 – 0.140 S1/2 2400
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
27.9 – 0.532 S
11,420 /S2
F.6.2
Rb/t
27.7 – 1.697 S1/2
b/t
15.2
7.3
19.0 – 0.530 S
15
2,417 /S2
b/t
15.2
7.3
19.0 – 0.530 S
12.6
155 /S
b/t
15.2
22.8
19.0 – 0.170 S
39
484 /S
ls
15.2
18.2
16.7 – 0.088 S
78
60,414 /S2
Rb/t
15.2
31.2
18.5 – 0.593 S1/2
leq
15.2
36.5
19.0 – 0.106 S
63
775 /S
b/t
19.7
54.9
27.9 – 0.150 S
93
1,298 /S
b/t
19.7
10.2
27.9 – 0.810 S
23
4,932 /S2
b/t
19.7
123.0
27.9 – 0.067 S
208
2,910 /S
leq
19.7
35.7
27.9 – 0.231 S
60
844 /S
b/t
9.1
38.7
11.5 – 0.062 S
76
38,665 /S2
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-30
E = 10,100 k/in2 kt = 1
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Extrusions and Pipe 2
G.2
F/ for S ≤ S1
S1
70
18.5 – 0.593 S1/2
35 189
189
F/ for S ≥ S2
3,776 /[S(1+S1/2/35)2]
3,776 /[S(1+S1/2/35)2]
January 2010
Table 2-22 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
6082 – T6, T6511
D.2b
23.1
D.2a
23.0
Fty = 38 k/in Fcy = 38 k/in2 Ftu = 45 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
23.0 29.9 26.9 29.9
J.3.7a, J.4.7 J.3.7b, J.7
46.2 30.7 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 29.9 see also F.4.2 26.9 see also F.6.2 29.9
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
22.1 – 0.144 S
63
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
26.0 – 0.141 S
75
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
26.0 – 0.271 S1/2 1545
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
44.4 – 1.064 S
11,420 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
E = 10,100 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Extrusions
G.2
42.8 – 3.027 S1/2
52
28.5 – 1.058 S1/2
28 131
3,776 /[S(1+S1/2/35)2]
b/t
23.0
6.5
29.8 – 1.039 S
12
2,417 /S2
b/t
23.0
6.5
29.8 – 1.039 S
10.0
194 /S
b/t
23.0
20.3
29.8 – 0.333 S
31
606 /S
ls
23.0
17.6
26.0 – 0.170 S
63
60,414 /S2
Rb/t
23.0
26.8
28.5 – 1.058 S1/2
leq
23.0
32.5
29.8 – 0.208 S
50
969 /S
b/t
29.9
48.0
44.4 – 0.301 S
74
1,635 /S
b/t
29.9
8.9
44.4 – 1.619 S
18
4,932 /S2
b/t
29.9
107.5
44.4 – 0.134 S
165
3,666 /S
leq
29.9
31.2
44.4 – 0.463 S
48
1,063 /S
b/t
13.8
34.5
18.0 – 0.122 S
60
38,665 /S2
131
3,776 /[S(1+S1/2/35)2]
VI-31
Table 2-23 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
6351 – T6
D.2b
21.5
D.2a
22.4
Fty = 37 k/in Fcy = 37 k/in2 Ftu = 42 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
21.5 29.2 26.2 29.2
J.3.7a, J.4.7 J.3.7b, J.7
43.1 28.6 Slenderness S
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 29.2 see also F.4.2 26.2 see also F.6.2 29.2
S2
kL/r
21.5 – 0.138 S
64
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
25.3 – 0.136 S
77
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
25.3 – 0.260 S1/2 1589
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
43.1 – 1.018 S
11,420 /S2
F.6.2
Rb/t
41.6 – 2.918 S1/2
b/t
22.4
6.6 29.0 – 0.996 S
12
2,417 /S2
b/t
22.4
6.6 29.0 – 0.996 S
10.2
191 /S
b/t
22.4
20.5 29.0 – 0.319 S
32
597 /S
ls
22.4
17.7 25.3 – 0.163 S
64
60,414 /S2
Rb/t
22.4
27.1
leq
22.4
32.8 29.0 – 0.199 S
51
956 /S
b/t
29.2
48.4 43.1 – 0.288 S
75
1,611 /S
b/t
29.2
9.0 43.1 – 1.549 S
19
4,932 /S2
b/t
29.2
108.5 43.1 – 0.128 S
168
3,612 /S
leq
29.2
31.5 43.1 – 0.442 S
49
1,047 /S
b/t
13.5
34.7
61
38,665 /S2
E.3
Elements—Flexural Compression flat elements supported on both B.5.5.1 edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-32
E = 10,100 k/in2 kt = 1
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported B.5.4.2 on both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Extrusions 2
G.2
F/ for S ≤ S1
S1
53
27.7 – 1.020 S1/2
27.7 – 1.020 S1/2
17.5 – 0.117 S
28 134
134
F/ for S ≥ S2
3,776 /[S(1+S1/2/35)2]
3,776 /[S(1+S1/2/35)2]
January 2010
Table 2-24 ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (UNWELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
7005 - T53
D.2b
25.6
D.2a
26.7
Fty = 44 k/in Fcy = 43 k/in2 Ftu = 50 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
25.6 34.7 31.2 34.7
J.3.7a, J.4.7 J.3.7b, J.7
51.3 34.1 Slenderness S
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 33.9 see also F.4.2 30.5 see also F.6.2 33.9
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
25.2 - 0.172 S
60
53,386 /S2
F.2.1
Lb/(ryeCb1/2)
29.7 - 0.169 S
72
90,441 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
29.7 - 0.324 S1/2 1409
24,534 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
50.9 - 1.282 S
11,873 /S2
F.6.2
Rb/t
48.6 - 3.547 S1/2
b/t
26.1
6.4
34.0 - 1.245 S
b/t
26.1
6.4
34.0 - 1.245 S
b/t
26.1
20.0
34.0 - 0.398 S
30
660 /S
ls
26.1
17.8
29.7 - 0.203 S
60
62,807 /S2
Rb/t
26.1
26.3
32.4 - 1.239 S1/2
leq
26.1
32.0
34.0 - 0.249 S
48
1,056 /S
b/t
33.9
46.9
50.9 - 0.362 S
70
1,786 /S
b/t
33.9
8.7
50.9 - 1.950 S
17
5,127 /S2
b/t
33.9
105.2
50.9 - 0.162 S
157
4,003 /S
leq
33.9
30.5
50.9 - 0.557 S
46
1,161 /S
b/t
16.0
33.7
21.1 - 0.152 S
57
40,196 /S2
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
E = 10,500 k/in2 kt = 1
kL/r
E.3
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported B.5.4.1 on one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Extrusions 2
G.2
49
32.4 - 1.239 S1/2
26 122 11
3,925 /[S(1+S1/2/35)2] 2,512 /S2
9.6 211 /S
122
3,925 /[S(1+S1/2/35)2]
VI-33
Table 2-1W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
1100 - H14
D.2b
5.6
D.2a
2.1
Fty = 3.5 k/in Fcy = 3.5 k/in2 Ftu = 11 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
2.1 2.8 2.5 2.8
J.3.7a, J.4.7 J.3.7b, J.7
11.3 7.5 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 2.8 see also F.4.2 2.5 see also F.6.2 2.8
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
1.9 – 0.004 S
284
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
2.2 – 0.004 S
341
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
2.2 – 0.008 S1/2 31534
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
3.4 – 0.022 S
11,420 /S2
F.6.2
Rb/t
3.9 – 0.124 S1/2
b/t
2.1
13.3
2.5 – 0.032 S
53
b/t
2.1
13.3
2.5 – 0.032 S
40.0 51 /S
b/t
2.1
41.6
2.5 – 0.010 S
125
159 /S
ls
2.1
23.8
2.2 – 0.005 S
284
60,414 /S2
Rb/t
2.1
80.1
2.6 – 0.053 S1/2
leq
2.1
66.6
2.5 – 0.006 S
200
255 /S
b/t
2.8
95.8
3.4 – 0.006 S
268
450 /S
b/t
2.8
17.8
3.4 – 0.034 S
66
4,932 /S2
b/t
2.8
214.8
3.4 – 0.003 S
601
1,008 /S
leq
2.8
62.3
3.4 – 0.010 S
174
292 /S
b/t
1.3
70.5
1.5 – 0.004 S
275
38,665 /S2
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-34
E = 10,100 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Sheet, Plate, Drawn Tube 2
G.2
332
2.6 – 0.053 S1/2
101 1379
1379
3,776 /[S(1+S1/2/35)2] 2,417 /S2
3,776 /[S(1+S1/2/35)2]
January 2010
Table 2-2W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
3003 – H14
Sheet, Plate, Drawn Tube
D.2b
7.2
E = 10,100 k/in2 kt = 1
D.2a
3.0
Fty = 5 k/in Fcy = 5 k/in2 Ftu = 14 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
3.0 3.9 3.5 3.9
J.3.7a, J.4.7 J.3.7b, J.7
14.4 9.5 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
2.8 – 0.008 S
236
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
3.2 – 0.008 S
284
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
3.2 – 0.015 S1/2 21836
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
4.9 – 0.039 S
11,420 /S2
F.6.2
Rb/t
5.6 – 0.203 S1/2
b/t
3.0
12.2
3.7 – 0.056 S
44
b/t
3.0
12.2
3.7 – 0.056 S
33.2 61 /S
b/t
3.0
38.0
3.7 – 0.018 S
104
192 /S
ls
3.0
23.4
3.2 – 0.009 S
236
60,414 /S2
Rb/t
3.0
70.3
3.8 – 0.086 S1/2
leq
3.0
60.9
3.7 – 0.011 S
166
307 /S
b/t
3.9
87.3
4.9 – 0.011 S
222
544 /S
b/t
3.9
16.2
4.9 – 0.060 S
55
4,932 /S2
b/t
3.9
195.7
4.9 – 0.005 S
497
1,219 /S
leq
3.9
56.8
4.9 – 0.017 S
144
353 /S
b/t
1.8
64.3
2.2 – 0.007 S
228
38,665 /S2
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 3.9 see also F.4.2 3.5 see also F.6.2 3.9
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
259
3.8 – 0.086 S1/2
84 1066
1066
3,776 /[S(1+S1/2/35)2] 2,417 /S2
3,776 /[S(1+S1/2/35)2]
VI-35
Table 2-3W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
3003 – H16
Sheet
D.2b
7.2
E = 10,100 k/in2 kt = 1
D.2a
3.0
Fty = 5 k/in Fcy = 5 k/in2 Ftu = 14 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
3.0 3.9 3.5 3.9
J.3.7a, J.4.7 J.3.7b, J.7
14.4 9.5 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
2.8 – 0.008 S
236
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
3.2 – 0.008 S
284
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
3.2 – 0.015 S1/2 21836
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
4.9 – 0.039 S
11,420 /S2
F.6.2
Rb/t
5.6 – 0.203 S1/2
b/t
3.0
12.2
3.7 – 0.056 S
44
b/t
3.0
12.2
3.7 – 0.056 S
33.2 61 /S
b/t
3.0
38.0
3.7 – 0.018 S
104
192 /S
ls
3.0
23.4
3.2 – 0.009 S
236
60,414 /S2
Rb/t
3.0
70.3
3.8 – 0.086 S1/2
leq
3.0
60.9
3.7 – 0.011 S
166
307 /S
b/t
3.9
87.3
4.9 – 0.011 S
222
544 /S
b/t
3.9
16.2
4.9 – 0.060 S
55
4,932 /S2
b/t
3.9
195.7
4.9 – 0.005 S
497
1,219 /S
leq
3.9
56.8
4.9 – 0.017 S
144
353 /S
b/t
1.8
64.3
2.2 – 0.007 S
228
38,665 /S2
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-36
see B.5.4.1 thru B.5.4.5 and E.4.2 3.9 see also F.4.2 3.5 see also F.6.2 3.9
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
259
3.8 – 0.086 S1/2
84 1066
1066
3,776 /[S(1+S1/2/35)2] 2,417 /S2
3,776 /[S(1+S1/2/35)2]
January 2010
Table 2-4W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
Alclad 3004 – H34
D.2b
10.8
D.2a
4.8
Fty = 8 k/in Fcy = 8 k/in2 Ftu = 21 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
4.8 6.3 5.7 6.3
J.3.7a, J.4.7 J.3.7b, J.7
21.5 14.3 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 6.3 see also F.4.2 5.7 see also F.6.2 6.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
4.5 – 0.016 S
185
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
5.3 – 0.016 S
222
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
5.3 – 0.030 S1/2 13413
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
8.1 – 0.083 S
11,420 /S2
F.6.2
Rb/t
9.2 – 0.389 S1/2
b/t
4.8
10.7
6.1 – 0.119 S
34
b/t
4.8
10.7
6.1 – 0.119 S
25.8 79 /S
b/t
4.8
33.6
6.1 – 0.038 S
81
ls
4.8
22.8
5.3 – 0.019 S
185
60,414 /S2
Rb/t
4.8
59.0
6.1 – 0.165 S1/2
715
3,776 /[S(1+S1/2/35)2]
leq
4.8
53.7
6.1 – 0.024S
129
395 /S
b/t
6.3
76.9
8.1 – 0.023 S
173
699 /S
b/t
6.3
14.3
8.1 – 0.127 S
43
4,932 /S2
b/t
6.3
172.3
8.1 – 0.010 S
387
1,567 /S
leq
6.3
50.0
8.1 – 0.036 S
112
455 /S
b/t
2.9
56.7
3.7 – 0.014 S
177
38,665 /S2
Elements—Flexural Compression flat elements supported on both B.5.5.1 edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
E = 10,100 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on both B.5.4.4 edges and with an intermediate stiffener curved elements supported on B.5.4.5 both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Sheet
G.2
187
6.1 – 0.165 S1/2
65 715
3,776 /[S(1+S1/2/35)2] 2,417 /S2
247 /S
VI-37
Table 2-5W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5005 – H14
Sheet and Plate
D.2b
7.7
E = 10,100 k/in2 kt = 1
D.2a
3.0
Fty = 5 k/in Fcy = 5 k/in2 Ftu = 15 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
3.0 3.9 3.5 3.9
J.3.7a, J.4.7 J.3.7b, J.7
15.4 10.2 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
2.8 – 0.008 S
236
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
3.2 – 0.008 S
284
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
3.2 – 0.015 S1/2 21836
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
4.9 – 0.039 S
11,420 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-38
see B.5.4.1 thru B.5.4.5 and E.4.2 3.9 see also F.4.2 3.5 see also F.6.2 3.9
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
5.6 – 0.203 S1/2 259
3.8 – 0.086 S1/2
84 1066
3,776 /[S(1+S1/2/35)2]
b/t
3.0
12.2
3.7 – 0.056 S
44
b/t
3.0
12.2
3.7 – 0.056 S
33.2 61 /S
b/t
3.0
38.0
3.7 – 0.018 S
104
192 /S
ls
3.0
23.4
3.2 – 0.009 S
236
60,414 /S2
Rb/t
3.0
70.3
3.8 – 0.086 S1/2
leq
3.0
60.9
3.7 – 0.011 S
166
307 /S
b/t
3.9
87.3
4.9 – 0.011 S
222
544 /S
b/t
3.9
16.2
4.9 – 0.060 S
55
4,932 /S2
b/t
3.9
195.7
4.9 – 0.005 S
497
1,219 /S
leq
3.9
56.8
4.9 – 0.017 S
144
353 /S
b/t
1.8
64.3
2.2 – 0.007 S
228
38,665 /S2
1066
2,417 /S2
3,776 /[S(1+S1/2/35)2]
January 2010
Table 2-6W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5005 – H32
Sheet and Plate
D.2b
7.7
E = 10,100 k/in2 kt = 1
D.2a
3.0
Fty = 5 k/in Fcy = 5 k/in2 Ftu = 15 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
3.0 3.9 3.5 3.9
J.3.7a, J.4.7 J.3.7b, J.7
15.4 10.2 Slenderness S
E.3
F/ for S ≤ S1
S1
kL/r
F/ for S1 < S < S2 2.8 – 0.008 S
236
51,352 /S2
284
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
F.4.2
(d/t)(Lb/(Cbd))1/2
F.6.2
Rb/t
5.6 – 0.203 S1/2
b/t
3.0
12.2
3.7 – 0.056 S
44
b/t
3.0
12.2
3.7 – 0.056 S
33.2 61 /S
b/t
3.0
38.0
3.7 – 0.018 S
104
192 /S
ls
3.0
23.4
3.2 – 0.009 S
236
60,414 /S2
Rb/t
3.0
70.3
3.8 – 0.086 S1/2
leq
3.0
60.9
3.7 – 0.011 S
166
307 /S
b/t
3.9
87.3
4.9 – 0.011 S
222
544 /S
b/t
3.9
16.2
4.9 – 0.060 S
55
4,932 /S2
b/t
3.9
195.7
4.9 – 0.005 S
497
1,219 /S
leq
3.9
56.8
4.9 – 0.017 S
144
353 /S
b/t
1.8
64.3
2.2 – 0.007 S
228
38,665 /S2
G.2
3.2 – 0.008 S
F/ for S ≥ S2
S2
Lb/(ryeCb1/2)
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 3.9 see also F.4.2 3.5 see also F.6.2 3.9
F.2.1
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
3.2 – 0.015 S1/2 21836 4.9 – 0.039 S 259
3.8 – 0.086 S1/2
84 1066
1066
23,599 /S 11,420 /S2 3,776 /[S(1+S1/2/35)2] 2,417 /S2
3,776 /[S(1+S1/2/35)2]
VI-39
Table 2-7W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5005 – H34
Sheet and Plate
D.2b
7.7
E = 10,100 k/in2 kt = 1
D.2a
3.0
Fty = 5 k/in Fcy = 5 k/in2 Ftu = 15 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
3.0 3.9 3.5 3.9
J.3.7a, J.4.7 J.3.7b, J.7
15.4 10.2 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
2.8 – 0.008 S
236
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
3.2 – 0.008 S
284
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
3.2 – 0.015 S1/2 21836
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
4.9 – 0.039 S
11,420 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-40
see B.5.4.1 thru B.5.4.5 and E.4.2 3.9 see also F.4.2 3.5 see also F.6.2 3.9
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
5.6 – 0.203 S1/2 259
3.8 – 0.086 S1/2
84 1066
3,776 /[S(1+S1/2/35)2]
b/t
3.0
12.2
3.7 – 0.056 S
44
b/t
3.0
12.2
3.7 – 0.056 S
33.2 61 /S
b/t
3.0
38.0
3.7 – 0.018 S
104
192 /S
ls
3.0
23.4
3.2 – 0.009 S
236
60,414 /S2
Rb/t
3.0
70.3
3.8 – 0.086 S1/2
leq
3.0
60.9
3.7 – 0.011 S
166
307 /S
b/t
3.9
87.3
4.9 – 0.011 S
222
544 /S
b/t
3.9
16.2
4.9 – 0.060 S
55
4,932 /S2
b/t
3.9
195.7
4.9 – 0.005 S
497
1,219 /S
leq
3.9
56.8
4.9 – 0.017 S
144
353 /S
b/t
1.8
64.3
2.2 – 0.007 S
228
38,665 /S2
1066
2,417 /S2
3,776 /[S(1+S1/2/35)2]
January 2010
Table 2-8W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5050 – H34
Sheet
D.2b
9.2
E = 10,100 k/in2 kt = 1
D.2a
3.6
Fty = 6 k/in Fcy = 6 k/in2 Ftu = 18 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
3.6 4.7 4.3 4.7
J.3.7a, J.4.7 J.3.7b, J.7
18.5 12.3 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
3.3 – 0.010 S
215
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
3.9 – 0.010 S
258
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
3.9 – 0.019 S1/2 18082
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
6.0 – 0.052 S
11,420 /S2
F.6.2
Rb/t
6.8 – 0.261 S1/2
b/t
3.6
11.6
4.5 – 0.075 S
40
b/t
3.6
11.6
4.5 – 0.075 S
30.1 68 /S
b/t
3.6
36.3
4.5 – 0.024 S
94
ls
3.6
23.2
3.9 – 0.012 S
215
60,414 /S2
Rb/t
3.6
65.7
4.5 – 0.111 S1/2
932
3,776 /[S(1+S1/2/35)2]
leq
3.6
58.0
4.5 – 0.015 S
150
339 /S
b/t
4.7
83.2
6.0 – 0.015 S
201
599 /S
b/t
4.7
15.4
6.0 – 0.080 S
50
4,932 /S2
b/t
4.7
186.4
6.0 – 0.007 S
451
1,343 /S
leq
4.7
54.1
6.0 – 0.023 S
131
390 /S
b/t
2.2
61.3
2.7 – 0.009 S
207
38,665 /S2
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 4.7 see also F.4.2 4.3 see also F.6.2 4.7
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
228
4.5 – 0.111 S1/2
76 932
3,776 /[S(1+S1/2/35)2] 2,417 /S2
212 /S
VI-41
Table 2-9W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5052 – H32
D.2b
12.8
D.2a
5.8
Fty = 9.5 k/in Fcy = 9.5 k/in2 Ftu = 25 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
5.8 7.5 6.7 7.5
J.3.7a, J.4.7 J.3.7b, J.7
25.6 17.1 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 7.5 see also F.4.2 6.7 see also F.6.2 7.5
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
5.4 – 0.021 S
170
51,860 /S2
F.2.1
Lb/(ryeCb1/2)
6.3 – 0.021 S
204
87,857 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
6.3 – 0.040 S1/2 11323
23,833 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
9.8 – 0.109 S
11,533 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on both B.5.5.1 edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on both B.5.5.3 edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-42
E = 10,200 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on one B.5.4.1 edge in all other columns and all beams flat elements supported on both B.5.4.2 edges flat elements supported on both B.5.4.4 edges and with an intermediate stiffener curved elements supported on B.5.4.5 both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Sheet, Plate, Drawn Tube 2
G.2
11.0 – 0.492 S1/2 167
7.3 – 0.209 S1/2
60 608
3,813 /[S(1+S1/2/35)2]
b/t
5.8
10.3
7.4 – 0.156 S
32
2,440 /S2
b/t
5.8
10.3
7.4 – 0.156 S
23.7 87 /S
b/t
5.8
32.2
7.4 – 0.050 S
74
ls
5.8
22.7
6.3 – 0.025 S
170
61,012 /S2
Rb/t
5.8
55.6
7.3 – 0.209 S1/2
608
3,813 /[S(1+S1/2/35)2]
leq
5.8
51.5
7.4 – 0.031 S
118
435 /S
b/t
7.5
73.6
9.8 – 0.031 S
158
771 /S
b/t
7.5
13.7
9.8 – 0.166 S
39
4,981 /S2
b/t
7.5
165.0
9.8 – 0.014 S
354
1,728 /S
leq
7.5
47.8
9.8 – 0.047 S
103
501 /S
b/t
3.5
54.4
4.4 – 0.018 S
162
39,048 /S2
272 /S
January 2010
Table 2-10W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5052 – H34
D.2b
12.8
D.2a
5.8
Fty = 9.5 k/in Fcy = 9.5 k/in2 Ftu = 25 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
5.8 7.5 6.7 7.5
J.3.7a, J.4.7 J.3.7b, J.7
25.6 17.1 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 7.5 see also F.4.2 6.7 see also F.6.2 7.5
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
5.4 – 0.021 S
170
51,860 /S2
F.2.1
Lb/(ryeCb1/2)
6.3 – 0.021 S
204
87,857 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
6.3 – 0.040 S1/2 11323
23,833 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
9.8 – 0.109 S
11,533 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
E = 10,200 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Sheet, Plate, and Drawn Tube 2
G.2
11.0 – 0.492 S1/2 167
7.3 – 0.209 S1/2
60 608
3,813 /[S(1+S1/2/35)2]
b/t
5.8
10.3
7.4 – 0.156 S
32
2,440 /S2
b/t
5.8
10.3
7.4 – 0.156 S
23.7 87 /S
b/t
5.8
32.2
7.4 – 0.050 S
74
ls
5.8
22.7
6.3 – 0.025 S
170
61,012 /S2
Rb/t
5.8
55.6
7.3 – 0.209 S1/2
608
3,813 /[S(1+S1/2/35)2]
leq
5.8
51.5
7.4 – 0.031 S
118
435 /S
b/t
7.5
73.6
9.8 – 0.031 S
158
771 /S
b/t
7.5
13.7
9.8 – 0.166 S
39
4,981 /S2
b/t
7.5
165.0
9.8 – 0.014 S
354
1,728 /S
leq
7.5
47.8
9.8 – 0.047 S
103
501 /S
b/t
3.5
54.4
4.4 – 0.018 S
162
39,048 /S2
272 /S
VI-43
Table 2-11W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5052 – H36
D.2b
12.8
D.2a
5.8
Fty = 9.5 k/in Fcy = 9.5 k/in2 Ftu = 25 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
5.8 7.5 6.7 7.5
J.3.7a, J.4.7 J.3.7b, J.7
25.6 17.1 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 7.5 see also F.4.2 6.7 see also F.6.2 7.5
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
5.4 – 0.021 S
170
51,860 /S2
F.2.1
Lb/(ryeCb1/2)
6.3 – 0.021 S
204
87,857 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
6.3 – 0.040 S1/2 11323
23,833 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
9.8 – 0.109 S
11,533 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-44
E = 10,200 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Sheet 2
G.2
21.4 – 0.492 S1/2 167
7.3 – 0.209 S1/2
60 608
3,813 /[S(1+S1/2/35)2]
b/t
5.8
10.3
7.4 – 0.156 S
32
2,440 /S2
b/t
5.8
10.3
7.4 – 0.156 S
23.7 87 /S
b/t
5.8
32.2
7.4 – 0.050 S
74
ls
5.8
22.7
6.3 – 0.025 S
170
61,012 /S2
Rb/t
5.8
55.6
7.3 – 0.209 S1/2
608
3,813 /[S(1+S1/2/35)2]
leq
5.8
51.5
7.4 – 0.031 S
118
435 /S
b/t
7.5
73.6
9.8 – 0.031 S
158
771 /S
b/t
7.5
13.7
9.8 – 0.166 S
39
4,981 /S2
b/t
7.5
165.0
9.8 – 0.014 S
354
1,728 /S
leq
7.5
47.8
9.8 – 0.047 S
103
501 /S
b/t
3.5
54.4
4.4 – 0.018 S
162
39,048 /S2
272 /S
January 2010
Table 2-12W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5083 – H116, H32, H321
heet and Plate S (0.188 to 1.500 in. thick)
D.2b
20.5
D.2a
10.9
Fty = 18 k/in2 Fcy = 18 k/in2 Ftu = 40 k/in2
E = 10,400 k/in2 kt = 1
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
10.9 14.2 12.8 14.2
J.3.7a, J.4.7 J.3.7b, J.7
41.0 27.3 Slenderness S
S2
kL/r
10.5 – 0.057 S
123
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
12.4 – 0.056 S
147
89,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
12.4 – 0.107 S1/2
5896
24,300 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
19.5 – 0.306 S
43
11,760 /S2
F.6.2
Rb/t
E.3
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 14.2 see also F.4.2 12.8 see also F.6.2 14.2
F/ for S1 < S < S2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
F/ for S ≤ S1
S1
21.4 – 1.191 S1/2 108
14.3 – 0.506 S1/2
336
F/ for S ≥ S2
3,888 /[S(1+S1/2/35)2]
b/t
10.9
8.7 14.7 – 0.433 S
23
b/t
10.9
8.7 14.7 – 0.433 S
16.9 124 /S
b/t
10.9
27.1 14.7 – 0.139 S
53
ls
10.9
21.8 12.4 – 0.067 S
123
62,208 /S2
Rb/t
10.9
44.0 14.3 – 0.506 S1/2
336
3,888 /[S(1+S1/2/35)2]
leq
10.9
43.4 14.7 – 0.087 S
b/t
14.2
61.6
19.5 – 0.086 S
113
1,100 /S
b/t
14.2
11.4
19.5 – 0.465 S
28
5,078 /S2
b/t
14.2
138.2
19.5 – 0.039 S
253
2,467 /S
leq
14.2
40.1
19.5 – 0.133 S
73
b/t
6.5
45.7
8.9 – 0.051 S
116
85
2,488 /S2
388 /S
620 /S
715 /S
39,813 /S2
VI-45
Table 2-13W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5086 – H34
Sheet, Plate, and Drawn Tube
D.2b
17.9
E = 10,400 k/in2 kt = 1
D.2a
8.5
Fty = 14 k/in Fcy = 14 k/in2 Ftu = 35 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
8.5 11.0 9.9 11.0
J.3.7a, J.4.7 J.3.7b, J.7
35.9 23.9 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
8.1 – 0.038 S
140
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
9.5 – 0.038 S
168
89,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
9.5 – 0.072 S1/2
7688
24,300 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
14.8 – 0.203 S
49
11,760 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-46
see B.5.4.1 thru B.5.4.5 and E.4.2 11.0 see also F.4.2 9.9 see also F.6.2 11.0
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
16.5 – 0.839 S1/2 129
11.0 – 0.357 S1/2
427
3,888 /[S(1+S1/2/35)2]
b/t
8.5
9.3 11.2 – 0.288 S
26
2,488 /S2
b/t
8.5
9.3 11.2 – 0.288 S
19.4 108 /S
b/t
8.5
29.2 11.2 – 0.092 S
61
ls
8.5
22.3 9.5 – 0.045 S
140
62,208 /S2
Rb/t
8.5
48.5 11.0 – 0.357 S1/2
427
3,888 /[S(1+S1/2/35)2]
leq
8.5
46.7 11.2 – 0.058 S
b/t
11.0
66.5
b/t
11.0
b/t
338 /S
97
541 /S
14.8 – 0.057 S
129
960 /S
12.3
14.8 – 0.309 S
32
5,078 /S2
11.0
148.9
14.8 – 0.026 S
290
2,151 /S
leq
11.0
43.2
14.8 – 0.088 S
84
b/t
5.1
49.2
6.8 – 0.034 S
133
624 /S
39,813 /S2
January 2010
Table 2-14W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5086 – H116 5086 – H32
Sheet and Plate Sheet and Plate, Drawn Tube
D.2b
17.9
D.2a
8.5
Fty = 14 k/in2 Fcy = 14 k/in2 Ftu = 35 k/in2
E = 10,400 k/in2 kt = 1
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
8.5 11.0 9.9 11.0
J.3.7a, J.4.7 J.3.7b, J.7
35.9 23.9 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
8.1 – 0.038 S
140
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
9.5 – 0.038 S
168
89,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
9.5 – 0.072 S1/2
7688
24,300 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
14.8 – 0.203 S
49
11,760 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 11.0 see also F.4.2 9.9 see also F.6.2 11.0
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
16.5 – 0.839 S1/2 129
11.0 – 0.357 S1/2
427
3,888 /[S(1+S1/2/35)2]
b/t
8.5
9.3 11.2 – 0.288 S
26
2,488 /S2
b/t
8.5
9.3 11.2 – 0.288 S
19.4 108 /S
b/t
8.5
29.2 11.2 – 0.092 S
61
ls
8.5
22.3 9.5 – 0.045 S
140
62,208 /S2
Rb/t
8.5
48.5 11.0 – 0.357 S1/2
427
3,888 /[S(1+S1/2/35)2]
leq
8.5
46.7 11.2 – 0.058 S
b/t
11.0
66.5
b/t
11.0
b/t
338 /S
97
541 /S
14.8 – 0.057 S
129
960 /S
12.3
14.8 – 0.309 S
32
5,078 /S2
11.0
148.9
14.8 – 0.026 S
290
2,151 /S
leq
11.0
43.2
14.8 – 0.088 S
84
b/t
5.1
49.2
6.8 – 0.034 S
133
624 /S
39,813 /S2
VI-47
Table 2-15W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5454 – H32
Sheet and Plate
D.2b
15.9
E = 10,400 k/in2 kt = 1
D.2a
7.3
Fty = 12 k/in Fcy = 12 k/in2 Ftu = 31 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
7.3 9.5 8.5 9.5
J.3.7a, J.4.7 J.3.7b, J.7
31.8 21.1 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
6.9 – 0.030 S
152
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
8.1 – 0.029 S
183
889,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
8.1 – 0.057 S1/2
F.4.2
(d/t)(Lb/(Cbd))1/2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-48
see B.5.4.1 thru B.5.4.5 and E.4.2 9.5 see also F.4.2 8.5 see also F.6.2 9.5
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
14.0 – 0.677 S1/2 144
9041
24,300 /S
12.6 – 0.158 S
53
11,760 /S2
9.3 – 0.288 S1/2
495
3,888 /[S(1+S1/2/35)2]
b/t
7.3
9.8 9.5 – 0.224 S
28
2,488 /S2
b/t
7.3
9.8 9.5 – 0.224 S
21.1 100 /S
b/t
7.3
30.5 9.5 – 0.072 S
66
ls
7.3
22.5 8.1 – 0.035 S
152
62,208 /S2
Rb/t
7.3
51.5 9.3 – 0.288 S1/2
495
3,888 /[S(1+S1/2/35)2]
leq
7.3
48.8 9.5 – 0.045 S
105
498 /S
b/t
9.5
69.5
12.6 – 0.045 S
141
883 /S
b/t
9.5
12.9
12.6 – 0.240 S
35
5,078 /S2
b/t
9.5
155.8
12.6 – 0.020 S
315
1,979 /S
leq
9.5
45.2
12.6 – 0.069 S
91
b/t
4.4
51.4
5.7 – 0.026 S
145
311 /S
574 /S
39,813 /S2
January 2010
Table 2-16W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
5454 – H34
Sheet and Plate
D.2b
15.9
E = 10,400 k/in2 kt = 1
D.2a
7.3
Fty = 12 k/in Fcy = 12 k/in2 Ftu = 31 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
7.3 9.5 8.5 9.5
J.3.7a, J.4.7 J.3.7b, J.7
31.8 21.1 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
6.9 – 0.030 S
152
52,877 /S2
F.2.1
Lb/(ryeCb1/2)
8.1 – 0.029 S
183
889,580 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
8.1 – 0.057 S1/2
F.4.2
(d/t)(Lb/(Cbd))1/2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 9.5 see also F.4.2 8.5 see also F.6.2 9.5
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
14.0 – 0.677 S1/2 144
9041
24,300 /S
12.6 – 0.158 S
53
11,760 /S2
9.3 – 0.288 S1/2
495
3,888 /[S(1+S1/2/35)2]
b/t
7.3
9.8 9.5 – 0.224 S
28
2,488 /S2
b/t
7.3
9.8 9.5 – 0.224 S
21.1 100 /S
b/t
7.3
30.5 9.5 – 0.072 S
66
ls
7.3
22.5 8.1 – 0.035 S
152
62,208 /S2
Rb/t
7.3
51.5 9.3 – 0.288 S1/2
495
3,888 /[S(1+S1/2/35)2]
leq
7.3
48.8 9.5 – 0.045 S
105
498 /S
b/t
9.5
69.5
12.6 – 0.045 S
141
883 /S
b/t
9.5
12.9
12.6 – 0.240 S
35
5,078 /S2
b/t
9.5
155.8
12.6 – 0.020 S
315
1,979 /S
leq
9.5
45.2
12.6 – 0.069 S
91
b/t
4.4
51.4
5.7 – 0.026 S
145
311 /S
574 /S
39,813 /S2
VI-49
Table 2-17W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
D.2b
12.3
D.2a
7.9 Tension
F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
7.9 10.2 9.2 10.2
J.3.7a, J.4.7 J.3.7b, J.7
24.6 16.4 Slenderness S
E.3
E = 10,100 k/in2 kt = 1
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 10.2 see also F.4.2 9.2 see also F.6.2 10.2
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
7.5 – 0.035 S
144
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
8.8 – 0.034 S
172
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
8.8 – 0.065 S1/2
8072
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
13.7 – 0.182 S
50
11,420 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-50
Fty = 13 k/in2 Fcy = 13 k/in2 Ftu = 24 k/in2
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
6005A - T61 Extrusions (up through 1.000 in. thick)
G.2
15.2 – 0.764 S1/2 133
10.2 – 0.325 S1/2
446
3,776 /[S(1+S1/2/35)2]
b/t
7.9
9.4 10.3 – 0.259 S
27
2,417 /S2
b/t
7.9
9.4 10.3 – 0.259 S
19.9 103 /S
b/t
7.9
29.4 10.3 – 0.083 S
62
ls
7.9
22.1 8.8 – 0.041 S
144
60,414 /S2
Rb/t
7.9
49.0 10.2 – 0.325 S1/2
446
3,776 /[S(1+S1/2/35)2]
leq
7.9
47.0 10.3 – 0.052 S
b/t
10.2
66.9
b/t
10.2
b/t
320 /S
99
513 /S
13.7 – 0.052 S
133
909 /S
12.4
13.7 – 0.278 S
33
4,932 /S2
10.2
150.0
13.7 – 0.023 S
298
2,037 /S
leq
10.2
43.5
13.7 – 0.079 S
86
b/t
4.7
49.5
6.2 – 0.030 S
136
591 /S
38,665 /S2
January 2010
Table 2-18W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateraltorsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
6061 – T6, T651, T6510, T6511
D.2b
12.3
D.2a
6.7
Fty = 11 k/in Fcy = 11 k/in2 Ftu = 24 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
6.7 8.7 7.8 8.7
J.3.7a, J.4.7 J.3.7b, J.7
24.6 16.4 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 8.7 see also F.4.2 Note 7.8 see also F.6.2 Welded with 4043, 5554, or 5654 8.7 and > 0.375” thick
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
6.3 – 0.027 S
157
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
7.4 – 0.026 S
188
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
7.4 – 0.050 S1/2
9618
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
11.4 – 0.139 S
55
11,420 /S2
F.6.2
Rb/t
8.5 – 0.257 S1/2
524
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported B.5.5.2 on tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate method B.5.5.4
January 2010
E = 10,100 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate method B.5.4.6
Elements—Shear flat elements supported on both edges
All Products (See note)
G.2
12.8 – 0.606 S1/2 150
3,776 /[S(1+S1/2/35)2]
b/t
6.7
9.8 8.6 – 0.198 S
29
b/t
6.7
9.8 8.6 – 0.198 S
21.8 94 /S
b/t
6.7
30.8 8.6 – 0.063 S
68
ls
6.7
22.3 7.4 – 0.031 S
157
60,414 /S2
Rb/t
6.7
52.2 8.5 – 0.257 S1/2
524
3,776 /[S(1+S1/2/35)2]
leq
6.7
49.2 8.6 – 0.040 S
109
468 /S
b/t
8.7
70.3 11.4 – 0.039 S
145
830 /S
b/t
8.7
13.0 11.4 – 0.212 S
36
4,932 /S2
b/t
8.7
157.5 11.4 – 0.018 S
326
1,861 /S
leq
8.7
45.7 11.4 – 0.060 S
94
b/t
4.0
51.9 5.2 – 0.023 S
149
2,417 /S2
293 /S
540 /S 38,665/S2
VI-51
Table 2-19W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
6061 – T6, T6510, T6511
D.2b
12.3
D.2a
9.1
Fty = 15 k/in Fcy = 15 k/in2 Ftu = 24 k/in2 2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
9.1 11.8 10.6 11.8
J.3.7a, J.4.7 J.3.7b, J.7
24.6 16.4 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 11.8 see also F.4.2 10.6 see also F.6.2 11.8
F/ for S ≤ S1
S1
Note: Welded with 5183, 5356, or 5556, or Welded with 4043, 5554, or 5654 and ≤0.375” thick
F/ for S1 < S < S2
F/ for S ≥ S2
S2
8.7 – 0.043 S
133
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
10.2 – 0.043 S
160
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
10.2 – 0.082 S1/2
6943
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
16.0 – 0.230 S
46
11,420 /S2
F.6.2
Rb/t
11.8 – 0.396S1/2
390
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-52
E = 10,100 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
All Products (See note)
G.2
17.7 – 0.933 S1/2 121
3,776 /[S(1+S1/2/35)2]
b/t
9.1
9.0
12.0 – 0.327 S
25
b/t
9.1
9.0
12.0 – 0.327 S
18.4 111 /S
b/t
9.1
28.2
12.0 – 0.105 S
58
ls
9.1
21.8
10.2 – 0.051 S
133
60,414 /S2
Rb/t
9.1
46.4
11.8 – 0.396 S1/2
390
3,776 /[S(1+S1/2/35)2]
leq
9.1
45.1
12.0 – 0.065 S
92
554 /S
b/t
11.8
64.2
16.0 – 0.065 S
123
982 /S
b/t
11.8
11.9
16.0 – 0.350 S
30
4,932 /S2
b/t
11.8
143.8
16.0 – 0.029 S
275
2,201 /S
leq
11.8
41.7
16.0 – 0.0100 S
80
b/t
5.5
47.5
7.3 – 0.038 S
126
2,417 /S2
346 /S
638 /S
38,665 /S2
January 2010
Table 2-20W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
6063 – T5 6063 – T52
Extrusions (Up thru 0.500 in. thick) Extrusions (Up thru 1.000 in. thick)
D.2b
8.7
D.2a
4.8
Fty = 8 k/in2 Fcy = 8 k/in2 Ftu = 17 k/in2
E = 10,100 k/in2 kt = 1
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
4.8 6.3 5.7 6.3
J.3.7a, J.4.7 J.3.7b, J.7
17.4 11.6 Slenderness S
E.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
4.5 – 0.016 S
185
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
5.3 – 0.016 S
222
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
5.3 – 0.030 S1/2
F.4.2
(d/t)(Lb/(Cbd))1/2
8.1 – 0.083 S
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
see B.5.4.1 thru B.5.4.5 and E.4.2 6.3 see also F.4.2 5.7 see also F.6.2 6.3
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Compression
G.2
9.2 – 0.389 S1/2 187
13413
23,599 /S
65
11,420 /S2
6.1 – 0.165 S1/2
715
3,776 /[S(1+S1/2/35)2]
b/t
4.8
10.7
6.1 – 0.119 S
34
2,417 /S2
b/t
4.8
10.7
6.1 – 0.119 S
25.8 79 /S
b/t
4.8
33.6
6.1 – 0.038 S
81
ls
4.8
22.8
5.3 – 0.019 S
185
60,414 /S2
Rb/t
4.8
59.0
6.1 – 0.165 S1/2
715
3,776 /[S(1+S1/2/35)2]
leq
4.8
53.7
6.1 – 0.024 S
129
395 /S
b/t
6.3
76.9
8.1 – 0.023 S
173
699 /S
b/t
6.3
14.3
8.1 – 0.127 S
43
4,932 /S2
b/t
6.3
172.3
8.1 – 0.010 S
387
1,567 /S
leq
6.3
50.0
8.1 – 0.036 S
112
455 /S
b/t
2.9
56.7
3.7 – 0.014 S
177
38,665 /S2
247 /S
VI-53
Table 2-21W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section D.2b
8.7
D.2a
4.8 Tension
F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
4.8 6.3 5.7 6.3
J.3.7a, J.4.7 J.3.7b, J.7
17.4 11.6 Slenderness S
E.3
Extrusions and Pipe
Fty = 8 k/in Fcy = 8 k/in2 Ftu = 17 k/in2
E = 10,100 k/in2 kt = 1
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 6.3 see also F.4.2 5.7 see also F.6.2 6.3
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
kL/r
4.5 – 0.016 S
185
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
5.3 – 0.016 S
222
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
5.3 – 0.030 S1/2
F.4.2
(d/t)(Lb/(Cbd))1/2
8.1 – 0.083 S
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-54
6063 – T6 2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
F/
G.2
9.2 – 0.389 S1/2 187
13413
23,599 /S
65
11,420 /S2
6.1 – 0.165 S1/2
715
3,776 /[S(1+S1/2/35)2]
b/t
4.8
10.7
6.1 – 0.119 S
34
2,417 /S2
b/t
4.8
10.7
6.1 – 0.119 S
25.8 79 /S
b/t
4.8
33.6
6.1 – 0.038 S
81
ls
4.8
22.8
5.3 – 0.019 S
185
60,414 /S2
Rb/t
4.8
59.0
6.1 – 0.165 S1/2
715
3,776 /[S(1+S1/2/35)2]
leq
4.8
53.7
6.1 – 0.024 S
129
395 /S
b/t
6.3
76.9
8.1 – 0.023 S
173
699 /S
b/t
6.3
14.3
8.1 – 0.127 S
43
4,932 /S2
b/t
6.3
172.3
8.1 – 0.010 S
387
1,567 /S
leq
6.3
50.0
8.1 – 0.036 S
112
455 /S
b/t
2.9
56.7
3.7 – 0.014 S
177
38,665 /S2
247 /S
January 2010
Table 2-22W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section D.2b
14.4
D.2a
9.7 Tension
F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
9.7 12.6 11.3 12.6
J.3.7a, J.4.7 J.3.7b, J.7
28.7 19.1 Slenderness S
E.3
Fty = 16 k/in Fcy = 16 k/in2 Ftu = 28 k/in2
Extrusions E = 10,100 k/in2 kt = 1
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 12.6 see also F.4.2 11.3 see also F.6.2 12.6
F/ for S ≤ S1
S1
F/ for S1 < S < S2
F/ for S ≥ S2
S2
kL/r
9.3 – 0.048 S
129
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
10.9 – 0.047 S
155
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
10.9 – 0.090 S1/2
6486
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
17.2 – 0.256 S
45
11,420 /S2
F.6.2
Rb/t
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
6082 – T6, T6511 2
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
F/
G.2
18.9 – 1.021 S1/2 115
12.6 – 0.434 S1/2
366
3,776 /[S(1+S1/2/35)2]
b/t
9.7
8.8 12.9 – 0.363 S
24
b/t
9.7
8.8 12.9 – 0.363 S
17.8 115 /S
b/t
9.7
27.7 12.9 – 0.116 S
56
ls
9.7
21.7 10.9 – 0.057 S
129
60,414 /S2
Rb/t
9.7
45.2 12.6 – 0.434 S1/2
366
3,776 /[S(1+S1/2/35)2]
leq
9.7
44.2 12.9 – 0.073 S
b/t
12.6
62.9
17.2 – 0.072 S
119
1,017 /S
b/t
12.6
11.7
17.2 – 0.389 S
29
4,932 /S2
b/t
12.6
141.1
17.2 – 0.032 S
266
2,280 /S
leq
12.6
40.9
17.2 – 0.111 S
77
b/t
5.8
46.6
7.8 – 0.043 S
122
89
2,417 /S2
358 /S
573 /S
661 /S
38,665 /S2
VI-55
Table 2-23W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
6351 – T6
D.2b
12.3
D.2a
6.7
Fty = 11 k/in Fcy = 11 k/in2 Ftu = 24 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
6.7 8.7 7.8 8.7
J.3.7a, J.4.7 J.3.7b, J.7
24.6 16.4 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 8.7 see also F.4.2 7.8 see also F.6.2 8.7
F/ for S ≤ S1
S1
Note: Welded with 4043, 5554, or 5654 filler and > 0.375” thick For other cases, use Table 2-19W
F/ for S1 < S < S2
F/ for S ≥ S2
S2
6.3 – 0.027 S
157
51,352 /S2
F.2.1
Lb/(ryeCb1/2)
7.4 – 0.026 S
188
86,996 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
7.4 – 0.050 S1/2
9618
23,599 /S
F.4.2
(d/t)(Lb/(Cbd))1/2
11.4 – 0.139 S
55
11,420 /S2
F.6.2
Rb/t
8.5 – 0.257 S1/2
524
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
VI-56
E = 10,100 k/in2 kt = 1
kL/r
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Extrusions (See note) 2
G.2
12.8 – 0.606 S1/2 150
3,776 /[S(1+S1/2/35)2]
b/t
6.7
9.8 8.6 – 0.198 S
29
2,417 /S2
b/t
6.7
9.8 8.6 – 0.198 S
21.8 94 /S
b/t
6.7
30.8 8.6 – 0.063 S
68
ls
6.7
22.3 7.4 – 0.031 S
157
60,414 /S2
Rb/t
6.7
52.2 8.5 – 0.257 S1/2
524
3,776 /[S(1+S1/2/35)2]
leq
6.7
49.2 8.6 – 0.040 S
109
468 /S
b/t
8.7
70.3
11.4 – 0.039 S
145
830 /S
b/t
8.7
13.0
11.4 – 0.212 S
36
4,932 /S2
b/t
8.7
157.5
11.4 – 0.018 S
326
1,861 /S
leq
8.7
45.7
11.4 – 0.060 S
94
b/t
4.0
51.9
5.2 – 0.023 S
149
293 /S
540 /S
38,665 /S2
January 2010
Table 2-24W ALLOWABLE STRESSES FOR BUILDING-TYPE STRUCTURES (WELDED) Allowable Stresses F/ (k/in2) Axial Tension axial tension stress on net effective area axial tension stress on gross area Flexure elements in uniform stress elements in flexure round tubes rods Bearing bolts or rivets on holes bolts on slots, pins on holes, flat surfaces Axial Compression all shapes member buckling Flexural Compression open shapes lateral-torsional buckling closed shapes lateral-torsional buckling rectangular bars lateral-torsional buckling round tubes local buckling
Section
F/
7005 – T53
D.2b
20.5
D.2a
14.5
Fty = 24 k/in Fcy = 24 k/in2 Ftu = 40 k/in2
Tension F.8.1.1 F.8.1.2, F.4.1 F.6.1 F.7
14.5 18.9 17.0 18.9
J.3.7a, J.4.7 J.3.7b, J.7
41.0 27.3 Slenderness S
E.3
Compression see B.5.4.1 thru B.5.4.5 and E.4.2 18.9 see also F.4.2 17.0 see also F.6.2 18.9
F/ for S ≤ S1
S1
kL/r
F/ for S1 < S < S2
S2
14.3 – 0.090 S 106
53,386 /S2
F.3.1
2LbSc/(Cb(IyJ)1/2)
16.8 – 0.169 S1/2
F.4.2
(d/t)(Lb/(Cbd))1/2
26.7 – 0.488 S
F.6.2
Rb/t
28.9 – 1.775 S1/2
b/t
14.5
8.0 20.1 – 0.690 S
19
b/t
14.5
8.0 20.1 – 0.690 S
14.5 146 /S
b/t
14.5
25.0 20.1 – 0.221 S
45
ls
14.5
21.3 16.8 – 0.106 S
106
62,807 /S2
Rb/t
14.5
39.5 19.3 – 0.755 S1/2
257
3,925 /[S(1+S1/2/35)2]
leq
14.5
40.0 20.1 – 0.138 S
73
729 /S
b/t
18.9
56.7 26.7 – 0.138 S
97
1,294 /S
b/t
18.9
10.5 26.7 – 0.742 S
24
5,127 /S2
b/t
18.9
127.1 26.7 – 0.062 S
217
2,901 /S
leq
18.9
36.8 26.7 – 0.212 S
63
b/t
8.7
42.1
G.2
16.8 – 0.088 S
F/ for S ≥ S2
Lb/(ryeCb1/2)
Elements—Flexural Compression flat elements supported on B.5.5.1 both edges flat elements supported on B.5.5.2 tension edge, compression edge free flat elements supported on B.5.5.3 both edges and with a longitudinal stiffener flat elements—alternate B.5.5.4 method
January 2010
E = 10,500 k/in2 kt = 1
F.2.1
Elements—Uniform Compression flat elements supported on B.5.4.1 one edge in columns whose buckling axis is not an axis of symmetry flat elements supported on B.5.4.1 one edge in all other columns and all beams flat elements supported on B.5.4.2 both edges flat elements supported on B.5.4.4 both edges and with an intermediate stiffener curved elements supported B.5.4.5 on both edges flat elements—alternate B.5.4.6 method
Elements—Shear flat elements supported on both edges
Extrusions 2
89
19.3 – 0.755 S1/2
12.1 – 0.081 S
127
90,441 /S2
4384
24,534 /S
37
11,873 /S2
257
100
3,925 /[S(1+S1/2/35)2] 2,512 /S2
456 /S
841 /S
40,196 /S2
VI-57
Table 3-1 RECOMMENDED MINIMUM BEND RADII FOR 90º COLD BENDS, SHEET AND PLATE Q W E R T RADII FOR VARIOUS THICKNESSES EXPRESSED IN TERMS OF THICKNESS “t” Alloy
Temper
1100
O H12 H14 H16 H18
0 0 0 0 1t
0 0 0 1 ⁄2t 1t
0 0 0 1t 11⁄2t
O T3 T4 T6
0 11⁄2t 11⁄2t 3t
0 21⁄2t 21⁄2t 4t
0 3t 3t 4t
O T3 T361Y T4 T81 T861Y
0 21⁄2t 3t 21⁄2t 41⁄2t 5t
0 3t 4t 3t 51⁄2t 6t
0 4t 5t 4t 6t 7t
2036
T4
..
1t
3003
O H12 H14 H16 H18
0 0 0 1 ⁄2t 1t
0 0 0 1t 11⁄2t
3004
O H32 H34 H36 H38
0 0 0 1t 1t
0 0 1t 1t 11⁄2t
3105
H25
1
5005
O H12 H14 H16 H18 H32 H34 H36 H38
2014
2024
5050
5052
5083
5086
VI-58
1
⁄64 in.
⁄2t
1
⁄32 in.
⁄2t
⁄16 in.
1
1
⁄8 in.
⁄16 in.
3
⁄4 in.
1
3
⁄8 in.
1
⁄2 in.
0 1 ⁄2t 1t 11⁄2t 21⁄2t
1
⁄2t 1t 1t 11⁄2t 3t
1t 1t 11⁄2t 21⁄2t 31⁄2t
1t 11⁄2t 2t 3t 4t
11⁄2t 2t 21⁄2t 4t 41⁄2t
1
⁄2t 4t 4t 5t
1t 5t 5t 6t
1t 5t 5t 8t
21⁄2t 6t 6t 81⁄2t
4t 7t 7t 91⁄2t
1
⁄2t 5t 6t 5t 71⁄2t 81⁄2t
1t 5t 6t 5t 8t 91⁄2t
1t 6t 8t 6t 9t 10t
21⁄2t 7t 81⁄2t 7t 10t 111⁄2t
4t 71⁄2t 91⁄2t 71⁄2t 101⁄2t 111⁄2t
1t
..
..
..
..
..
0 0 0 1t 2t
0 1 ⁄2t 1t 11⁄2t 21⁄2t
1
⁄2t 1t 1t 21⁄2t 31⁄2t
1t 1t 11⁄2t 3t 41⁄2t
1t 11⁄2t 2t 31⁄2t 51⁄2t
11⁄2t 2t 21⁄2t 4t 61⁄2t
0 1 ⁄2t 1t 11⁄2t 21⁄2t
1
⁄2t 1t 11⁄2t 21⁄2t 3t
1t 1t 11⁄2t 3t 4t
1t 11⁄2t 21⁄2t 31⁄2t 5t
1t 11⁄2t 21⁄2t 4t 51⁄2t
11⁄2t 2t 3t 41⁄2t 61⁄2t
1
1
..
..
..
..
..
0 0 0 1 ⁄2t 1t 0 0 1 ⁄2t 1t
0 0 0 1t 11⁄2t 0 0 1t 11⁄2t
0 0 0 1t 2t 0 0 1t 2t
⁄2t
0 1 ⁄2t 1t 11⁄2t 21⁄2t 1 ⁄2t 1t 11⁄2t 21⁄2t
1
⁄2t 1t 11⁄2t 21⁄2t 31⁄2t 1t 11⁄2t 21⁄2t 31⁄2t
1t 1t 11⁄2t 3t 41⁄2t 1t 11⁄2t 3t 41⁄2t
1t 11⁄2t 2t 31⁄2t 51⁄2t 11⁄2t 2t 31⁄2t 51⁄2t
11⁄2t 2t 21⁄2t 4t 61⁄2t 2t 21⁄2t 4t 61⁄2t
O H32 H34 H36 H38
0 0 0 1t 1t
0 0 0 1t 11⁄2t
0 0 1t 11⁄2t 21⁄2t
1
⁄2t 1t 11⁄2t 2t 3t
1t 1t 11⁄2t 21⁄2t 4t
1t 11⁄2t 2t 3t 5t
11⁄2t .. .. .. ..
11⁄2t .. .. .. ..
O H32 H34 H36 H38
0 0 0 1t 1t
0 0 1t 1t 11⁄2t
0 1t 11⁄2t 11⁄2t 21⁄2t
1
⁄2t 11⁄2t 2t 21⁄2t 3t
1t 11⁄2t 2t 3t 4t
1t 11⁄2t 21⁄2t 31⁄2t 5t
11⁄2t 11⁄2t 21⁄2t 4t 51⁄2t
11⁄2t 2t 3t 41⁄2t 61⁄2t
O H321
.. ..
.. ..
1
⁄2t 1t
1t 11⁄2t
1t 11⁄2t
1t 11⁄2t
11⁄2t 2t
11⁄2t 21⁄2t
O H32 H34 H36
0 0 1 ⁄2t 11⁄2t
0 1 ⁄2t 1t 2t
1
⁄2t 1t 11⁄2t 21⁄2t
1t 11⁄2t 2t 3t
1t 11⁄2t 21⁄2t 31⁄2t
1t 2t 3t 4t
11⁄2t 21⁄2t 31⁄2t 41⁄2t
11⁄2t 3t 4t 5t
January 2010
Table 3-1 RECOMMENDED MINIMUM BEND RADII FOR 90º COLD BENDS, SHEET AND PLATE Q W E R T (Continued) RADII FOR VARIOUS THICKNESSES EXPRESSED IN TERMS OF THICKNESS “t” Alloy
Temper
5154
O H32 H34 H36 H38
0 0 1 ⁄2t 1t 11⁄2t
H25 H28
⁄64 in.
1
⁄32 in.
1
⁄16 in.
1
1
⁄8 in.
⁄16 in.
3
⁄4 in.
1
3
⁄8 in.
1
⁄2 in.
0 1 ⁄2t 1t 11⁄2t 21⁄2t
1
⁄2t 1t 11⁄2t 2t 3t
1t 11⁄2t 2t 3t 4t
1t 11⁄2t 21⁄2t 31⁄2t 5t
1t 2t 3t 4t 5t
1 ⁄2t 21⁄2t 31⁄2t 41⁄2t 61⁄2t
11⁄2t 31⁄2t 4t 5t 61⁄2t
0 1t
0 11⁄2t
1t 21⁄2t
2t 3t
.. ..
.. ..
.. ..
.. ..
0 0 1 ⁄2t 1t 11⁄2t
0 1 ⁄2t 1t 11⁄2t 21⁄2t
1
5254
O H32 H34 H36 H38
⁄2t 1t 11⁄2t 2t 3t
1t 11⁄2t 2t 3t 4t
1t 11⁄2t 21⁄2t 31⁄2t 5t
1t 2t 3t 4t 5t
11⁄2t 21⁄2t 31⁄2t 41⁄2t 61⁄2t
11⁄2t 31⁄2t 4t 5t 61⁄2t
O H32 H34
0 1 ⁄2t 1 ⁄2t
1
5454
1
⁄2t ⁄2t 1t
1t 1t 11⁄2t
1t 2t 2t
1t 2t 21⁄2t
11⁄2t 21⁄2t 3t
11⁄2t 3t 31⁄2t
2t 4t 4t
5456
O H321
.. ..
.. ..
1t ..
1t 2t
11⁄2t 2t
11⁄2t 21⁄2t
2t 3t
2t 31⁄2t
5457
O
0
0
0
..
..
..
..
..
O H32 H34 H36 H38
0 0 0 1t 1t
0 0 1t 1t 11⁄2t
0 1t 11⁄2t 11⁄2t 21⁄2t
1
⁄2t 11⁄2t 2t 21⁄2t 3t
1t 11⁄2t 2t 3t 4t
1t 11⁄2t 21⁄2t 31⁄2t 5t
1 ⁄2t 11⁄2t 21⁄2t 4t 51⁄2t
11⁄2t 2t 3t 41⁄2t 61⁄2t
H25 H28
0 1t
0 11⁄2t
0 21⁄2t
1t 3t
.. ..
.. ..
.. ..
.. ..
6061
O T4 T6
0 0 1t
0 0 1t
0 1t 11⁄2t
1t 11⁄2t 21⁄2t
1t 21⁄2t 3t
1t 3t 31⁄2t
11⁄2t 31⁄2t 41⁄2t
2t 4t 5t
7050
T7
..
..
..
..
..
8t
9t
91⁄2t
7072
O H14 H18
0 0 1t
0 0 1t
.. .. ..
.. .. ..
.. .. ..
.. .. ..
.. .. ..
.. .. ..
7075
O T6
0 3t
0 4t
1t 5t
1t 6t
11⁄2t 6t
21⁄2t 8t
31⁄2t 9t
4t 91⁄2t
7178
O T6
0 3t
0 4t
1t 5t
11⁄2t 6t
11⁄2t 6t
21⁄2t 8t
31⁄2t 9t
4t 91⁄2t
5252
5652 5657
1
1
Q The radii listed are the minimum recommended for bending sheets and plates without fracturing in a standard press brake with air bend dies. Other types of bending operations may require larger radii or permit smaller radii. The minimum permissible radii will also vary with the design and condition of the tooling. W Alclad sheet in the heat-treatable alloys can be bent over slightly smaller radii than the corresponding tempers of the bare alloy. E Heat-treatable alloys can be formed over appreciably smaller radii immediately after solution heat treatment. R The H112 temper (applicable to non-heat treatable alloys) is supplied in the as-fabricated condition without special property control but usually can be formed over radii applicable to the H14 (or H34) temper or smaller. T The reference test method is ASTM E290. Y Tempers T361 and T861 formerly designated T36 and T86, respectively.
January 2010
VI-59
Table 3-2 RECOMMENDED MINIMUM INSIDE RADII FOR 180º COLD BENDS, WIRE AND ROD*
Table 3-3 SHEET THICKNESS FOR 180º COLD BENDING (METAL TO METAL)*
VI-60
January 2010
January 2010
VI-61
Inside Radius of Bend (in.)
Table 3-4 DEVELOPED LENGTH OF MATERIAL FOR 90º BENDS
VI-62
January 2010
Inside Radius of Bend (in.)
Table 3-4 DEVELOPED LENGTH OF MATERIAL FOR 90º BENDS (Continued)
Table 4-1 ALLOWABLE UNIFORM BEAM LOADS* Aluminum Association Standard Channels, 6061-T6 Span (ft)
*Total uniformly distributed load W applied at the beam’s neutral axis on a simply supported single span braced against twisting, calculated using the section properties listed in Part V, Table 4, the allowable stresses for building-type structures given in Part VI, Table 2-19, and rye from Part I, Section F.2.2.1.
January 2010
VI-63
Table 4-2 ALLOWABLE UNIFORM BEAM LOADS* Aluminum Association Standard I-Beams, 6061-T6 SPAN (FT)
*Total uniformly distributed load W applied at the beam’s neutral axis on a simply supported single span braced against twisting, calculated using the section properties listed in Part V, Table 8, the allowable stresses for building-type structures given in Part VI, Table 2-19, and rye from Part I, Section F.2.2.1.
VI-64
January 2010
Table 4-3 ALLOWABLE LOADS ON ALUMINUM TREAD PLATE Tread Plate is sheet or plate having a raised figure pattern on one surface to provide improved traction
January 2010
VI-65
Table 4-4 MAXIMUM SPANS (IN.) Commercial Corrugated and w Roofing and Siding Number of Equal Spans Design Load (psf)
One Strength
Two Deflection
Three
Strength
Deflection
Strength
Deflection
Corrugated Roofing and Siding—0.024” thick 20
79
61
79
–
88
76
25
70
57
70
–
79
70
30
64
54
64
–
72
66
35
60
51
60
–
67
63
40
56
49
56
–
63
60
45
53
47
53
–
59
58
50
50
45
50
–
56
56
Corrugated Roofing and Siding—0.032” thick 20
92
67
92
90
102
83
25
82
63
82
–
92
77
30
75
59
75
–
84
73
35
70
56
70
–
78
69
40
65
54
65
–
73
66
45
62
52
62
–
69
64
50
58
50
58
–
65
62
128
–
144
136
V-Beam Roofing and Siding—0.032” thick, 4 7/8” Pitch 20
128
110
25
115
102
115
–
129
127
30
105
97
105
–
118
–
35
98
92
98
–
109
–
40
92
88
92
–
102
–
45
86
85
86
–
97
–
50
82
82
82
–
92
–
55
78
–
78
–
87
–
60
75
–
75
–
84
–
V-Beam Roofing and Siding—0.040” thick, 4 7/8” Pitch 20
150
118
150
–
167
146
25
134
110
134
–
150
136
30
123
104
123
–
137
128
35
114
99
114
–
127
122
40
107
94
107
–
119
117
45
101
91
101
–
113
112
50
96
88
96
–
107
–
55
91
85
91
–
102
–
60
87
83
87
–
98
–
V-Beam Roofing and Siding—0.050” thick, 4 7/8” Pitch
VI-66
20
171
127
171
170
191
157
25
154
118
154
–
172
146
30
141
111
141
–
158
138
35
131
106
131
–
146
131
40
122
102
122
–
137
125
January 2010
Table 4-4 MAXIMUM SPANS (IN.) (Continued) Commercial Corrugated and V-Beam Roofing and Siding Number of Equal Spans Design Load (psf)
One Strength
Two Deflection
Strength
Three Deflection
Strength
Deflection
116
–
129
121
V-Beam Roofing and Siding—0.050” thick, 4 7/8” Pitch (continued) 45
116
98
50
110
94
110
–
123
117
55
105
92
105
–
117
113
60
100
89
100
–
112
110
128
–
143
141
V-Beam Roofing and Siding—0.032” thick, 5 1/3” Pitch 20
128
114
25
115
106
115
–
129
–
30
105
100
105
–
118
–
35
98
95
98
–
109
–
40
91
91
91
–
102
–
45
86
–
86
–
96
–
50
82
–
82
–
91
–
55
78
–
78
–
87
–
60
75
–
75
–
84
–
V-Beam Roofing and Siding—0.040” thick, 5 1/3” Pitch 20
153
123
153
–
171
151
25
137
114
137
–
154
141
30
126
108
126
–
141
133
35
117
102
117
–
130
126
40
109
98
109
–
122
121
45
103
94
103
–
115
–
50
98
91
98
–
110
–
55
93
88
93
–
104
–
60
90
86
90
–
100
–
V-Beam Roofing and Siding—0.050” thick, 5 1/3” Pitch 20
176
132
176
176
197
163
25
158
123
158
–
177
151
30
145
116
145
–
162
143
35
134
110
134
–
150
136
40
126
105
126
–
141
130
45
119
101
119
–
133
125
50
113
98
113
–
126
121
55
108
95
108
–
120
117
60
103
92
103
–
115
114
1. Maximum spans are calculated in accordance with the Specification for Aluminum Structures for allowable strength design of building-type structures. 2. Material is Alclad 3004-H151, -H261, or -H361 (which are stucco embossed tempers) or Alclad 3004-H16. Dimensions are given in Part V Table 25 and section properties are given in Part V Table 26. 3. The deflection limit is 1/60 of the span.
January 2010
VI-67
Table 4-5 MAXIMUM SPANS (IN.) COMMERCIAL RIBBED SIDING Design Load (psf)
Number of Equal Spans One Strength1
Strength2
Two
Deflection1
Three
Deflection2
Strength1
Strength2
Deflection1
Deflection2
Strength1
Strength2
Deflection1
Deflection2
Ribbed Siding—0.032” thick, 4” Pitch 20
98
101
85
101
98
–
113
110
106
25
88
91
79
91
88
–
101
98
98
30
80
83
75
83
80
–
93
90
93
35
75
77
71
77
75
–
86
83
–
40
70
72
68
72
70
–
80
78
–
45
66
68
66
68
66
–
76
74
–
50
63
64
63
64
63
–
72
70
–
Ribbed Siding—0.040” thick, 4” Pitch 20
118
120
92
120
118
–
134
132
113
25
106
107
85
107
106
–
120
118
105
30
97
98
80
98
97
–
110
108
99
35
90
91
76
91
90
–
102
100
94
40
84
85
73
85
84
–
95
94
90
45
79
80
70
80
79
–
90
89
87
50
75
76
68
76
75
–
85
84
84
Ribbed Siding—0.032” thick, 8” Pitch 20
62
77
74
–
77
62
–
–
78
69
–
–
25
56
69
–
–
69
56
–
–
70
62
–
–
30
51
63
–
–
63
51
–
–
64
57
–
–
35
47
59
–
–
59
47
–
–
59
53
–
–
40
44
55
–
–
55
44
–
–
55
49
–
–
45
42
52
–
–
52
42
–
–
52
47
–
–
50
40
49
–
–
49
40
–
–
49
44
–
–
Ribbed Siding—0.040” thick, 8” Pitch 20
75
91
80
84
91
75
–
–
94
84
–
–
25
67
82
74
79
82
67
–
–
84
75
–
–
30
62
75
70
74
75
62
–
–
77
69
–
–
35
57
69
67
–
69
57
–
–
71
64
–
–
40
54
65
64
–
65
54
–
–
67
60
–
–
45
51
61
–
–
61
51
–
–
63
56
–
–
50
48
58
–
–
58
48
–
–
60
54
–
–
1. Wide flat is on loaded side; load is toward neutral axis. 2. Narrow flat is on loaded side; load is toward neutral axis. 3. Maximum spans are calculated in accordance with the Specification for Aluminum Structures for allowable strength design of building-type structures. 4. Material is Alclad 3004-H151, -H261, or -H361 (which are stucco embossed tempers) or Alclad 3004-H16. Dimensions are given in Part V Table 25 and section properties are given in Part V Table 26. 5. The deflection limit is 1/60 of the span.
VI-68
January 2010
Table 5-1 NOMINAL TENSILE AND SINGLE SHEAR STRENGTHS FOR 2024-T4 AND 7075-T73 MACHINE SCREWS Nominal Minor Diameter (in.)
2024-T4
7075-T73
Tensile Strength (lb)
Shear Strength (lb)
Nominal Size
Basic Major Diameter D (in.)
4
0.112
40
UNC
0.0822
329
361
196
218
4
0.112
48
UNF
0.0872
370
406
221
245
5
0.125
40
UNC
0.0952
442
484
264
292
5
0.125
44
UNF
0.0979
467
512
279
309
6
0.138
32
UNC
0.1008
495
542
295
327
6
0.138
40
UNF
0.1082
570
626
340
377
8
0.164
32
UNC
0.1268
783
858
467
518
Threads/in. n
2024-T4
7075-T73
8
0.164
36
UNF
0.1309
835
915
498
552
10
0.190
24
UNC
0.1404
960
1050
573
635
10
0.190
32
UNF
0.1528
1140
1250
678
752
12
0.216
24
UNC
0.1664
1350
1480
804
891
12
0.216
28
UNF
0.1735
1470
1610
874
969
1/4
0.250
20
UNC
0.1905
1770
1940
1050
1170
1/4
0.250
28
UNF
0.2075
2100
2300
1250
1390
5/16
0.3125
18
UNC
0.2463
2950
3240
1760
1950
5/16
0.3125
24
UNF
0.2629
3360
3690
2010
2230
3/8
0.375
16
UNC
0.3006
4400
4820
2630
2910
3/8
0.375
24
UNF
0.3254
5160
5650
3080
3410
1. UNC = Unified National Course Thread Series; UNF = Unified National Fine Thread Series 2. Area at root of threads (Ar) used to compute strengths using the nominal minor diameter for external threads (Class 2A) given in ASME B1.1-1989; Ar = (p/4)(D - 1.191/n)2 3. Obtain design strengths by dividing the strengths in this table by the appropriate safety factor or multiplying by the appropriate resistance factor (see Part I). 4. Strengths in this table were computed using: for 2024-T4, Ftu = 62 ksi and Fsu = 37 ksi; for 7075-T73, Ftu = 68 ksi and Fsu = 41 ksi.
January 2010
VI-69
Table 5-2 NOMINAL SINGLE SHEAR STRENGTHS FOR 2024-T4 AND 7075-T73 TYPE AB AND B SHEET METAL SCREWS Shear Strength (lb) Nominal Size
2024-T4
7075-T73
4
195
216
5
235
260
6
285
316
7
345
382
8
391
433
10
529
586
12
716
793
14
995
1100
1. Obtain design strengths by dividing the strengths in this table by the appropriate safety factor or multiplying by the appropriate resistance factor (see Part I). 2. Strengths in this table were computed using: for 2024-T4, Fsu = 37 ksi; for 7075-T73, Fsu = 41 ksi.
Table 5-3 NOMINAL TENSILE AND SINGLE SHEAR STRENGTHS FOR 2024-T4 AND 7075-T73 BOLTS AND CAP SCREWS Nominal Size
Basic Major Diameter D (in.)
Single Shear Strength (lb) Threads/ in. n
10
0.190
24
Tensile Strength (lb) 2024-T4 960
7075-T73
Threads in Shear Plane 2024-T4
1050
573
7075-T73 635
No Threads in Shear Plane 2024-T4 1050
7075-T73 1160
1/4
0.250
20
1770
1940
1050
1170
1820
2010
5/16
0.3125
18
2950
3240
1760
1950
2840
3140
3/8
0.375
16
4400
4820
2630
2910
4090
4530
1/2
0.500
13
8120
8910
4850
5370
7260
8050
5/8
0.625
11
13,000
14,300
7760
8600
11,400
12,600
3/4
0.750
10
19,400
21,300
11,600
12,800
16,300
18,100
7/8
0.875
9
26,900
29,500
16,000
17,800
22,200
24,700
1
1.000
8
35,300
38,700
21,100
23,300
29,100
32,200
1. Class 2A external threads, UNC (Unified National Course Thread Series) 2. Area at root of threads (Ar) used to compute strengths for tension and single shear with threads in shear plane using the nominal minor diameter for external threads (Class 2A) given in ASME B1.1-1989; Ar = (p/4)(D - 1.191/n)2. Area of basic major diameter (p/4)D2 used to compute strengths for single shear with no threads in shear plane. 3. Obtain design strengths by dividing the strengths in this table by the appropriate safety factor or multiplying by the appropriate resistance factor (see Part I). 4. Strengths in this table were computed using: for 2024-T4, Ftu = 62 ksi and Fsu = 37 ksi; for 7075-T73, Ftu = 68 ksi and Fsu = 41 ksi.
VI-70
January 2010
Table 5-4 BOLT DIMENSIONS
January 2010
VI-71
Table 5-4 BOLT DIMENSIONS (Continued)
VI-72
January 2010
Table 5-5 NUT DIMENSIONS
Table 5-6 INTERNAL THREAD STRIPPING AREA FOR CLASS 2B UNC THREADS
January 2010
Nominal Size Threads/in.
Nominal Diameter (in.)
Internal Thread Stripping Area Asn (in2/in. of engagement)
8–32
0.164
0.334
10–24
0.190
0.401
12–24
0.216
0.458
1/4–20
0.250
0.539
5/16–18
0.3125
0.682
3/8–16
0.375
0.828
VI-73
Table 6-1 ASD ALLOWABLE TENSILE STRESSES FOR GROOVE WELDS (BUILDING-TYPE STRUCTURES) Filler 1100
4043
5.6
12.3
5183
5356
5554
5556
5654
21.5
15.4
Filler allowable tensile stress (ksi) (note 1) Base Metal 5.6
5.6
3003
7.2
5.6
7.2
Alclad 3003
6.7
5.6
6.7
3004 Alclad 3004 5005 5050 5052 5083 5086 5154 5454 5456 6005, 6005A 6061, 6351 6063, 6463
VI-74
Base metal allowable tensile stress (ksi) (note 2)
1100
20.5
17.9
15.9
5.6
11.3
11.3
11.3
11.3
10.8
10.8
10.8
10.8
7.7
7.7
7.7
7.7
7.7
9.2
9.2
9.2
9.2
9.2
12.8
12.8
12.8
12.8
20.0
20.0
17.9
17.9
17.9
15.4
15.4
15.4
15.9
15.9
15.9
20.0
20.5
21.0
17.9 15.4 15.9
15.4
15.9 21.0
12.3
12.3
12.3
12.3
12.3
12.3
12.3
12.3
12.3
12.3
8.7
8.7
8.7
8.7
8.7
6082
14.4
12.3
14.4
14.4
14.4
7005
20.5
20.5
17.9
20.5
January 2010
Table 6-1M ASD ALLOWABLE TENSILE STRESSES FOR GROOVE WELDS (BUILDING-TYPE STRUCTURES) Filler 1100
4043
38
85
5183
5356
5554
5556
5654
149
105
Filler allowable tensile stress (MPa) (note 1) Base Metal
141
123
77
77
77
77
74
74
74
74
38
38
38
3003
49
38
49
Alclad 3003
46
38
46
3004 Alclad 3004 5005 5050 5052 5083 5086 5154 5454 5456 6005, 6005A 6061, 6351 6063, 6463
Base metal allowable tensile stress (MPa) (note 2)
1100
110
54
54
54
54
54
64
64
64
64
64
87
87
87
87
138
138
123
123
123
105
105
105
110
110
110
138
141
146
123 105 110
105
110 146
85
85
85
85
85
85
85
85
85
85
59
59
59
59
59
6082
97
85
97
97
97
7005
141
141
123
141
Notes for Table 6-1 and 6-1M: 1. Allowable tensile stress for filler = Ftuw/1.95 2. Allowable tensile stress for base metal = Ftuw/1.95 3. Allowable stresses are for the base metal welded to itself. 4. Bold values indicate the filler governs the joint strength.
January 2010
VI-75
Table 6-2 ASD ALLOWABLE SHEAR STRESSES FOR FILLET WELDS (BUILDING-TYPE STRUCTURES) Filler 1100
4043
3.8
5.9
5183
5356
5554
5556
5654
10.3
6.2
Filler allowable shear stress (ksi) (note 1) Base Metal
8.7
10.2
10.2
8.7
10.2
9.4
9.4
8.7
9.4 6.5
3.8
5.8
3003
7.3
3.8
5.9
Alclad 3003
7.3
3.8
5.9
3004 5005 5050 5052 5083 5086 5154 5454 5456
Base metal allowable shear stress (ksi) (note 2)
5.8
Alclad 3004
8.7
6.5
5.9
6.5
6.5
8.7
5.9
8.7
8.7
8.7
11.6
10.8
8.7
10.3
16.7
10.8
15.2
10.8
8.7
13.8
10.8
8.7
13.8
10.8
8.7
10.3
10.8
18.1
10.3 10.3 8.7
10.3
5.9
10.8
8.7
10.3
10.9
5.9
10.8
8.7
10.3
6063, 6463
8.0
5.9
8.0
8.0
8.0
6082
10.9
5.9
10.8
8.7
10.3
7005
16.0
10.8
8.7
10.3
6061, 6351
6.2
10.3
10.9
6005, 6005A
VI-76
10.8
1100
January 2010
Table 6-2M ASD ALLOWABLE SHEAR STRESSES FOR FILLET WELDS (BUILDING-TYPE STRUCTURES) Filler 1100
4043
26
41
5183
5356
5554
5556
5654
72
44
Filler allowable shear stress (MPa) (note 1) Base Metal
74
59
69
69
59
69
65
65
59
65
40
26
40
3003
51
26
41
Alclad 3003
51
26
41
3004 Alclad 3004 5005 5050 5052 5083 5086 5154 5454 5456 6005, 6005A 6061, 6351
Base metal allowable shear stress (MPa) (note 2)
1100
59
45
41
45
45
45
62
41
62
59
62
80
74
59
72
116
74
105
74
59
72
94
74
59
94
74
59
74
123
72 72 59
72
76
41
74
59
72
76
41
74
59
72
54
41
54
54
54
6082
76
41
74
59
72
7005
112
74
59
72
6063, 6463
44
72
Notes for Table 6-2 and 6-2M: 1. Allowable shear stress for filler = Fsuw/1.95 2. Allowable shear stress for base metal = Fsuw/(1.95 cos45°) 3. Allowable stresses are for the base metal welded to itself. 4. Bold values indicate the filler governs the joint strength. 5. Compute stresses on the effective throat of the fillet.
January 2010
VI-77
Table 6-3 LRFD DESIGN TENSILE STRESSES FOR GROOVE WELDS (BUILDING-TYPE STRUCTURES) Filler 1100
4043
8.3
18.0
5183
5356
5554
5556
5654
31.5
22.5
Filler design tensile stress (ksi) (note 1) Base Metal
26.3
16.5
16.5
16.5
16.5
15.8
15.8
15.8
15.8
8.3
8.3
3003
10.5
8.3
10.5
Alclad 3003
9.8
8.3
9.8
3004 5005 5050 5052 5083 5086 5154 5454 5456 6005, 6005A 6061, 6351
Base metal design tensile stress (ksi) (note 2)
8.3
Alclad 3004
VI-78
30.0
1100
23.3
11.3
11.3
11.3
11.3
11.3
13.5
13.5
13.5
13.5
13.5
18.8
18.8
18.8
18.8
30.0
30.0
26.3
26.3
26.3
22.5
22.5
22.5
23.3
23.3
23.3
30.0
30.0
31.5
26.3 22.5 23.3
22.5
23.3 31.5
18.0
18.0
18.0
18.0
18.0
18.0
18.0
18.0
18.0
18.0
6063, 6463
12.8
12.8
12.8
12.8
12.8
6082
21.0
18.0
21.0
21.0
21.0
7005
30.0
30.0
26.3
30.0
January 2010
Table 6-3M LRFD DESIGN TENSILE STRESSES FOR GROOVE WELDS (BUILDING-TYPE STRUCTURES) Filler 1100
4043
56
124
5183
5356
5554
5556
5654
218
154
Filler design tensile stress (MPa) (note 1) Base Metal 56
56
56
3003
71
56
71
Alclad 3003
68
56
68
3004 Alclad 3004 5005 5050 5052 5083 5086 5154 5454 5456 6005, 6005A 6061, 6351
Base metal design tensile stress (MPa) (note 2)
1100
206
180
161
113
113
113
113
109
109
109
109 79
79
79
79
79
94
94
94
94
94
128
128
128
128
203
203
180
180
180
154
154
154
161
161
161
203
206
214
180 154 161
154
161 214
124
124
124
124
124
124
124
124
124
124
6063, 6463
86
86
86
86
86
6082
143
124
143
143
143
7005
206
206
180
206
Notes for Table 6-3 and 6-3M: 1. Design tensile stress for filler = 0.75Ftuw 2. Design tensile stress for base metal = 0.75Ftuw 3. Design stresses are for the base metal welded to itself. 4. Bold values indicate the filler governs the joint strength.
January 2010
VI-79
Table 6-4 LRFD DESIGN SHEAR STRESSES FOR FILLET WELDS (BUILDING-TYPE STRUCTURES) Filler 1100
4043
5.6
8.6
5183
5356
5554
5556
5654
15.0
9.0
Filler design shear stress (ksi) (note 1) Base Metal 1100
8.5
5.6
8.5
12.8
12.8
10.6
5.6
8.6
10.6
5.6
8.6
3004
14.8
14.8
12.8
14.8
13.8
13.8
12.8
13.8
5005 5050 5052 5083 5086 5154 5454 5456
Base metal design shear stress (ksi) (note 2)
3003 Alclad 3003 Alclad 3004
9.5
8.6
9.5
9.5
9.5
12.7
8.6
12.7
12.7
12.7
17.0
15.8
12.8
15.0
25.5
15.8
22.3
15.8
12.8
20.2
15.8
12.8
20.2
15.8
12.8
15.0
15.8
27.6
15.0 15.0 12.8
15.0
8.6
15.8
12.8
15.0
15.9
8.6
15.8
12.8
15.0
6063, 6463
11.7
8.6
11.7
11.7
11.7
6082
15.9
8.6
15.8
12.8
15.0
7005
23.3
15.8
12.8
15.0
6061, 6351
9.0
15.0
15.9
6005, 6005A
VI-80
15.8
January 2010
Table 6-4M LRFD DESIGN SHEAR STRESSES FOR FILLET WELDS (BUILDING-TYPE STRUCTURES) Filler 1100
4043
38
60
5183
5356
5554
5556
5654
105
64
Filler design shear stress (MPa) (note 1) Base Metal
109
86
101
101
86
101
95
95
86
95 66
58
38
58
3003
74
38
60
Alclad 3003
74
38
60
3004 Alclad 3004 5005 5050 5052 5083 5086 5154 5454 5456
Base metal design shear stress (MPa) (note 2)
1100
86
66
60
66
66
90
60
90
86
90
117
109
86
105
175
109
154
109
86
138
109
86
138
109
86
105
109
180
105 105 86
105
111
60
109
86
105
111
60
109
86
105
6063, 6463
80
60
80
80
80
6082
111
60
109
86
105
7005
164
109
86
105
6005, 6005A 6061, 6351
64
105
Notes for Table 6-4 and 6-4M: 1. Design shear stress for filler = 0.75Fsuw 2. Design shear stress for base metal = 0.75Fsuw/cos45° 3. Design stresses are for the base metal welded to itself. 4. Bold values indicate the filler governs the joint strength. 5. Compute stresses on the effective throat of the fillet.
January 2010
VI-81
BEAM FORMULAS
VI-82
January 2010
January 2010
VI-83
VI-84
January 2010
January 2010
VI-85
VI-86
January 2010
CASE 12A.
Trapezoidally distributed load: Total Load: W = w(L – a) Max. Load: w lb/in Reactions: R1 = W/2, R2 = W/2 Shear Forces: V1 = R1; V2 = -R2 Maximum bending moment = ___ w ( 3L2 – 4a2 ), x = __ L
24
2
Maximum deflection =
[
(L) ]
4 a 2 + 16 __ a 4 , x = __ _______ wL 25 – 40 __ L
1920EI
January 2010
(L)
2
VI-87
VI-88
January 2010
January 2010
VI-89
VI-90
January 2010
January 2010
VI-91
VI-92
January 2010
January 2010
VI-93
VI-94
January 2010
January 2010
VI-95
VI-96
January 2010
January 2010
VI-97
VI-98
January 2010
January 2010
VI-99
Aluminum Design Manual
PART VII Illustrative Examples
VII Illustrative Examples This part of the Design Manual illustrates the use of the Specification for Aluminum Structures, Part I of the Design Manual. Terms and symbols used in Part VII are consistent with those used in the Specification for Aluminum Structures, which should be consulted for their definitions. References in Part VII to section and table numbers are to the section and table numbers in the Specification for Aluminum Structures.
TABLE OF CONTENTS Example 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
January 2010
Type of Member Rod, round Strap, rectangular I beam Tube, square Tube, round Plate Rivets Pin I beam Box section, latticed Wide flange section Tube, square Tube, square with stiffeners Tube, round I beam Girder, welded Welded girder, transverse stiffeners Tube, round Bar, rectangular Tube, rectangular I beam Unsymmetric shape Channel Welded beam Welded beam, stiffened web I beam Welded connection Curtainwall beam Formed sheet Tapping screw connection I beam
Type of Load Tension, axial Tension, axial Bending Bending Bending Bending Bearing Bearing Compression, axial Compression, axial Compression, axial Compression, axial Compression, axial Compression, axial Bending Bending Bending Bending Bending Bending Bending Bending Bending Bending Bending Shear Shear Bending Bending, shear Shear, tension Bending
Page VII 6 7 8 10 12 13 15 16 18 20 22 24 26 27 28 30 34 36 37 39 41 43 45 47 48 49 51 52 58 61 62
VII-3
CORRELATION OF SPECIFICATION SECTIONS AND ILLUSTRATIVE EXAMPLES Type of Stress ELEMENTS IN UNIFORM COMPRESSION
Type of Member and Element
Section No.*
Main Examples
Other Examples
Flat elements supported on one edge
B.5.4.1
10, 11, 21
3, 9, 13 16, 22, 23, 26
Flat elements supported on both edges
B.5.4.2
12, 22
4, 9, 11, 20, 24, 29
Curved elements supported on both edges
B.5.4.5
14
12
Flat elements supported on tension edge, compression edge free
B.5.5.2
23
Flat elements supported on both edges
B.5.5.1
24
Flat elements supported on both edges and with a longitudinal stiffener
B.5.5.3
25
TENSION, axial
All tension members
D.2
1
2
COMPRESSION, axial
All columns
E.3
9
10, 11, 12, 14
FLEXURE
Open shapes
F.2
15, 16, 17
3, 21, 22, 23, 26, 28
Round tubes
F.6
18
5
Rods
F.7
19
6
ELEMENTS IN FLEXURE
3, 16, 20, 21, 22, 23
Closed shapes
F.3
20
4
SHEAR
Flat elements supported on both edges
G.2
26
3, 4, 15, 20, 21, 22, 23
BEARING
On rivets
J.4.7
7
On flat surfaces and pins
J.7
8
*The section number refers to the type of stress and member used and corresponds to the number in the Specification for Aluminum Structures.
In the following examples, widths of elements are conservatively calculated ignoring the effect of corner fillets. For example, in example 3 the flange element width b, used to calculate the allowable stress in the flange of I 5 × 3.70, is calculated from the face of the web as shown in Figure i
Figure i
January 2010
VII-5
Example 1 ROD IN AXIAL TENSION Illustrating Section D.2
Figure 1 GIVEN: 1. Tensile load: 4.50 k (4,500 lb). 2. Alloy: 6061-T6. 3. Structure type: building.
REQUIRED:
From Part V, Table 28, the required diameter for A = 0.231 in2: 2 ___ pD = 0.231 in2
4
___
√
________
4(0.231) ________ D = ___ 4A = 0.542 in. p =
√
p
Diameter of smallest standard rod that will safely resist the load.
A 3/4 in. diameter rod has a minor diameter of 0.642 in. at the net section (at the threads), so use D = 3/4 in.
SOLUTION:
NOTE: Long slender members have little resistance to lateral loads. Therefore, tension members with large slenderness ratios L/r should be avoided unless such members can also resist vibration and lateral loads such as wind, dead load, and the weight of workmen and equipment.
From Part VI Table 2-19, Section D.2: Allowable tensile stress: The net section allowable stress is less than the gross section allowable stress and the net section is less than the gross section, so only the net section needs to be considered. F/Ω = 19.5 ksi on the net section Given load P = 4.50 k P = ________ Required area A = ___ 4.50 k = 0.231 in2 F/W 19.5 k/in2
VII-6
January 2010
Example 2 RECTANGULAR STRAP IN AXIAL TENSION Illustrating Section D.2
Figure 2 GIVEN: 1. Tensile load: 1.20 k (1,200 lb). 2. Alloy: 5052-H36. 3. Structure type: building.
REQUIRED: Thickness of a 1 in. wide strap which will safely resist the load. Assume that the ends of the strap are connected so that the net section is sufficiently large that it does not govern the tensile strength of the strap.
Reading Fty from Table A.3.4 as 29 ksi, the required gross area is Ag = Pn Ωt /Fty = (1.20 k)(1.65)/(29 k/in2) = 0.0683 in2 The required thickness for 1.00 in. width is t = 0.0683 in2/(1.00 in.) = 0.0683 in. From Part V, Table 3, the minimum standard thickness ≥ 0.0683 in. is t = 0.071 in.
SOLUTION: From Section D.2, the allowable tensile strength for yielding in the gross section is Pn = Fty Ag /Ωt = 1.20 k
January 2010
VII-7
Example 3 I-BEAM IN BENDING Illustrating Sections F.2, F.8, G.2
Figure 3 GIVEN: 1. Uniform load of 4.50 k/ft (4,500 lb/ft) including dead load. 2. Beam length 16 ft with continuous lateral support. 3. Vertical support spacing 4 ft o.c. (first support at end of beam). 4. Alloy: 6061-T6. 5. Structure type: building.
Section F.2, open shapes, requires that for open shapes not subject to lateral-torsional buckling, the nominal flexural strength be determined using Section F.8. For tension, from Part VI Table 2-19, conservatively using F.8.1.1 (for the flanges which are in uniform tension) since it gives a lesser strength than F.8.1.2 (for the web, which is in flexure), the allowable tensile bending stress is F/Ω = 19.5 ksi
REQUIRED:
Required section modulus S:
Size of lightest Aluminum Association standard I-beam that will safely support the load.
S = M/(F/Ω) = (92.6 in-k)/(19.5 k/in2) = 4.75 in3 From Part V, Table 8
SOLUTION: From Part VI Beam Formulas Case 43 continuous beam of four equal spans, uniformly distributed load:
Now check the beam for compression according to Section F.8.2.
Load w = (4.50 k/ft)(ft/12 in.) = 0.375 k/in. The maximum bending moment is M = -168 wL /1568 = -168(0.375 k/in.)(48 in) /1568 = -92.6 in-k 2
2
The negative sign for the bending moment M indicates that the top flange of the beam is in tension. The point of maximum stress is at the first interior support. VII-8
Select trial I-beam I 5 × 3.70 Sx = 5.58 in3
a) The flange is in uniform compression, so according to Section F.8.2.1, the strength is given in Section B.5.4. Section B.5.4.1 addresses flat elements supported on one edge; from Part VI, Table 2-19 b/t = (3.50 - 0.19)/[(2)(0.32)] = 5.2 < 6.7 = S1, so F/Ω = 21.2 ksi January 2010
b) Section F.8.2.2 refers to Section B.5.5 for the strength of the web in flexure. Section B.5.5.1 addresses flat elements supported on both edges. Since the beam is symmetric about the bending axis, cc = - co, and m = 0.65. b/t = (5.00 - 2(0.32))/0.19 = 22.9 < S1, = 49.3, so F/Ω = 27.6 ksi The allowable bending stress is therefore governed by tension (F/W = 19.5 ksi) Web shear is addressed by Section G.2, flat webs supported on both edges. b/t = 22.9 < 35.3 = S1, so Fs /Ω = 12.7 ksi, allowable shear stress From Part VI Beam Formulas Case 43, continuous beam of four equal spans. V = 17 wL/28 = 17(0.375 k/in)(48 in)/28 = 10.9 k, maximum web shear The required web area is A = V/(Fs /W) = (10.9 k)/ (12.7 k/in2) = 0.86 in2
January 2010
(The above is an approximate method. See example 26.) For I 5 × 3.70 Aw = dtw = (5.00) 0.19 = 0.95 in2 > 0.86 in2 The I 5 × 3.70 is therefore the lightest satisfactory beam. NOTES: The building code should be checked to see if analysis for other loading conditions (such as alternate span loading) is required in addition to the load addressed above. Generally, the use of the formula M = ± wL2/8 satisfies all building code requirements for uniformly loaded beams supported on both ends. If holes will be drilled in the flange at or near points of high tensile stress, it may be necessary to use a larger beam. This may be determined by multiplying the computed flange stress at the section under consideration by the ratio of the gross area of the flange to the net area of the flange and comparing the result with the allowable stress. Web crippling at supports should be checked; see Example 4.
VII-9
Example 4 SQUARE TUBE IN BENDING Illustrating Sections F.8.1, F.8.2, G.2, and J.8.1
Figure 4 GIVEN: 1. Concentrated load of 1.50 k (1,500 lb) including dead load, applied at mid span. 2. Span 40 in., simply supported 3. Alloy: 6063-T6 4. Structure type: building
REQUIRED: Thickness of a standard 3 in. square tube that will safely support the load.
SOLUTION: From Part VI Beam Formulas Case 1, a simply supported beam with a concentrated load P at the center, the maximum bending moment = M = PL/4 = (1.5 k)(40 in.)/4 = 15.0 in-k A square tube is not subject to lateral-torsional buckling, so Section F.3, Tubular Shapes, requires that the nominal flexural strength be determined from Section F.8. For tensile bending, the allowable tensile bending stress can be conservatively determined as the lesser of F.8.1.1 (for the flanges) and F.8.1.2 (for the webs), which is F.8.1.1 From Part VI, Design Aids, Table 2-21, F/W = 15.2 ksi Required section modulus S: S = M/F = (15.0 in-k)/(15.2 k/in2) = 0.99 in3 Part V, Table 23, shows that a 3 × 3 × 0.125 square tube has a section modulus S = 1.32 in3, which exceeds the required section modulus for tension, so select this as a trial size. VII-10
For compression bending in a square tube, Section F.8.2.1, Elements in Uniform Compression, governs; this section refers to Section B.5.4. From Part VI, Table 2-21, Section B.5.4.2, flat elements supported on both edges: b/t = (3-2(0.125))/0.125 = 22 ≤ S1 = 22.8 Fb /Ω = 15.2 ksi; bending stress is satisfactory. For shear in the web, Part VI Beam Formulas Case 1 gives V = P/2 = (1.5k)/2 = 0.75 k From Part VI, Table 2-21, Section G.2 gives the allowable shear stress. b/t = 22.0 < 38.7 = S1, so Fs/Ω = 9.1 ksi Area of webs, A = 2 × 0.125 × (3.00 - 2 × 0.125) = 0.687 in2 Approximate web shear stress fs = V/A = (0.75 k)/(0.687 in2) = 1.1 k/in2 < 9.1 k/in2 (See example 26 for a discussion of the accuracy of this method.) Use 3 in. × 0.125 in. hollow square tubing. NOTES: A lighter tube in 6061-T6 alloy would be satisfactory structurally; however, for architectural uses,
January 2010
6063-T6 may be preferred because of its superior finishing characteristics.
where
____
Cwa = t2 sinq(0.46Fcy + 0.02√ EFcy ) ___________ = (0.125)2 sin 90° (0.46 (25) + 0.02√(10,000)(25) ) = 0.337 k Cwb = Cw3 + Ri (1 - cos q) Cw3 = 0.4 in. Cwb = 0.4 + 0(1 - cos 90) = 0.4 in. Cw2 = 1.3 in.
The supports and load point of Figure 4 are shown as sharp, a condition seldom used in actual practice but used here to define the span length more clearly. In an actual installation, the forces on the beam will be distributed over a distance N, which must be large enough to prevent local crippling of the webs. So Section J.8.1 addresses Crippling of Flat Webs. From Table A.3.4, Fcy = 25 ksi, E = 10,100 ksi Ri = 0 for extruded shapes t = 0.125 in., θ = 90°, Try N = 0.10 in. The allowable reaction Rn/W for concentrated forces applied at a distance from the member end that is less than the member depth divided by 2 is
Rn/W = (1.2)(0.337)(0.10 + 1.3)/[(0.4)(1.95)] Rn/W = 0.726 k allowable, per web. For two webs the end reaction per web is V/2 = 0.75/2 = 0.375 k 0.375 k < 0.726 k; therefore a bearing length of 0.10 in. is satisfactory
Rn/W = (1.2Cwa)(N + Cw2)/[(Cwb)(Ω)]
January 2010
VII-11
Example 5 PIPE IN BENDING Illustrating Sections F.6.1, F.6.2 Load = 25 lb/ft2 = 0.025 k/ft2 P = 0.025 × 3.00 × 4.00 = 0.30 k L = (15 + 0.5 × 3) × 12 = 198 in. M1 = PL = 0.30 × 198 = 59.4 in-k This is the portion of the total load moment due to wind load on the sign and must be corrected later when the pipe size is known for the additional moment caused by wind load on the pipe. Trial section modulus M ____ S = ____ 1 = 59.4 = 5.60 in3 F/Ω 10.6 From Part V, Table 26, a trial pipe size is obtained.
Figure 5 GIVEN: 1. Wind load 25 lb/ft2 on 3 ft high signboard, the bottom of which is 15 ft above the base of the supporting pipes, and 20.1 lb/ft2 on the supports. See Figure 5. 2. Support: Schedule 40 standard pipes spaced as shown in Figure 5. 3. Alloy: 6061-T6 4. Base: Welded with 5356 filler 5. Structure type: building
REQUIRED: Size of standard pipe to safely resist the load
SOLUTION: Table A.3.5 gives the properties for welded 6061-T6 as: Ftu = 24 ksi, Fty = 15 ksi, Fcy = 15 ksi From Section F.6.1 the allowable bending stress in the pipe for the limit states of yielding and rupture at the welded base is the lesser of 1.17Fcy /W = (1.17)(15 ksi)/1.65 = 10.6 ksi and 1.17Fty /W = (1.17)(15 ksi)/1.65 = 10.6 ksi and 1.24Ftu /W = (1.24)(24 ksi)/1.95 = 15.3 ksi; 10.6 ksi controls. From Part VI, Beam Formulas Case 14, concentrated load, P, at free end of cantilever beam: The load from the sign is not actually a concentrated load as in the beam diagram, however, the moment at the base is correctly determined using the resultant of the sign force acting at the center of the sign. VII-12
6 in. Schedule 40, S = 8.50 in3, OD = 6.63 in., t = 0.280 in. Adding the moment due to wind load on the pipe, from Case 16, cantilever beams, uniformly distributed load of w k/in. w = (0.0201)(6.63)/(144) = 0.000925 k/in. M2 = wL2/2 = (0.000925)[(15)(12)]2/2 = 15.0 in-k Total moment M = M1 + M2 = 59.4 + 15.0 = 74.4 in-k f = __ M = ____ 74.4 = 8.8 ksi < 10.6 ksi S 8.50 Size selected is satisfactory for yielding and rupture. Section F.6.2 addresses local buckling in round tubes. (6.63 - 0.280)/2 Rb/t = _____________ = 11.3 0.280 Taking buckling constants from Part VI, Table 1-2, for welded 6061-T6
(
) (
)
Btb- 1.17Fcy 2 29.2 - (1.17)(15) 2 S1= ___________ = ______________ = 57 > 11.3 Dtb 1.538 —— —— so Fb/W = Btb - Dtb√ Rb /t = 29.2 - 1.538√ 11.3 = 24.0 ksi; (24.0 ksi)/1.65 = 14.5 ksi > 8.8 ksi; so the size is satisfactory. Use 6 in. Schedule 40 pipe. NOTE: The axial stress in the supports due to dead load is assumed to be negligible in comparison to the reserve strength available; however, if the sign is very heavy, the effect should be considered. January 2010
Example 6 PLATE IN BENDING Illustrating Section F.4.1
Figure 6 GIVEN: 1. Load 0.400 k (400 lb), along a line at the center of a plate. 2. Plate: 24 in. wide, spanning 36 in. 3. Alloy: 6061-T6 4. Structure type: building
REQUIRED:
The required section modulus is S = M/(F/Ω) = (3.6)/27.6 = 0.130 in3 From Part VI, Table 28, the section modulus of rectangle is S = bd 2/6 where b = 24 in. and d = t1 Solving for t1 __
________
√b √
Minimum standard thickness to support the load safely without deflecting more than 3⁄8 in.
6(0.130) t1= ___ 6S = ________ = 0.18 in.
SOLUTION:
Deflection From Part VI Beam Formulas Case 1
From Part VI Table 2-18, for elements in flexure Section F.4.1: Allowable tensile stress F/Ω = 27.6 ksi Section F.4.1. Allowable compressive stress Fb /Ω = 27.6 ksi From Part VI, Beam Formulas Case 1, simply supported beam, concentrated load P at center M = PL/4 = (0.4)(36)/4 = 3.60 in-k January 2010
24
Deflection = PL3/(48 EI) A correction is required for plates because individual fibers are restricted in the way they can change shape in the direction perpendicular to the stress. They can change in vertical dimension but not in horizontal dimension. The correction is: PL3(1 - n2) Deflection = D = _________ 48EI where n = Poisson’s ratio, given in Table A.3.1 as 0.33. VII-13
From Part V Table 28 the moment of inertia for a rectangle is bt3 I = ___ 2 12 Section L.3 requires that bending deflections be determined using the compression modulus of elasticity from Table A.3.4, in which E = 10,100 ksi
Since t2 > t1 deflection controls; use 3/8 in. thick plate. NOTES: The rails supporting the plate are assumed to have been checked structurally to see that they will safely support the load. They should be fastened to the plate at intervals to prevent spreading. The loading and deflection limits in this problem differ from those for Part VI Table 4-3.
Combining the equations for I and D, __________
__________________
L3(1 - n2) 3 __________________ P (0.4)363(1 - 0.332) t2= _________ = = 4bED 4(24)(10,100)(0.375)
√
3
√
= 0.36 in., based on limiting deflection to 0.375 in..
VII-14
January 2010
Example 7 BEARING ON RIVETS Illustrating Section J.4 The allowable shear per inch is (0.32 k)/(3 in.) = 0.11 k/ in. > 0.09 k/in. Section J.4.7 gives the rivet’s allowable bearing as Rn/Ω = detFtu /Ω = (3)(0.063)(37)/1.95 = 3.59 k but shall not exceed 2Dht Ftu = 2(0.191)(0.063)(37) = 0.89 k The allowable bearing per inch is (0.89 k)/(3 in.) = 0.30 k/in. > 0.09 k/in. Since both bearing and shear are satisfactory, the connection will adequately resist the shear load.
Figure 7 GIVEN: 1. Rivets: 3/16 in. diameter, cold-driven, 2117-T4 before driving, spaced 3 in. on centers, edge distance 0.375 in., in a 0.191 in. hole. 2. Sheet: 0.063 in., 5052-H36 alloy. 3. Corner post extrusion considerably thicker than the sheet and with equivalent unit bearing strength. 4. Load: 0.090 k/in. shear (90 lb/in.). 5. Structure type: building
REQUIRED: Check the strength of the connection for compliance with the Specification for Aluminum Structures.
SOLUTION: The rivet spacing meets the requirements of Section J.4.3 because it exceeds 3 times the rivet diameter (3(3/16) = 9/16 < 3). The hole diameter meets the requirements of Section J.4.2 because it is no more than 4% greater than the rivet diameter (0.191/(3/16) = 1.02) Section J.4.6 gives the rivet’s allowable shear strength as Rn/Ω = π Dh2Fsu /(4Ω) = π(0.191)2(26)/(4(2.34)) = 0.32 k January 2010
VII-15
Example 8 BEARING ON A PIN Illustrating Section J.7
Figure 8 GIVEN: 1. Beam: Hollow rectangular tube 4 in. × 6 in. with wall thickness 0.080 in. 2. End supports: Aluminum Association standard 5 in. × 2.25 in. channel (CS5 × 2.21). 3. Beam load: 1.20 k (1,200 lb) uniformly distributed. 4. Pin: Allowable bending stress 25 ksi. 5. Beam and end support alloy: 6063-T5. 6. Structure type: building
REQUIRED: The minimum pin size for the end connection.
SOLUTION: From Part VI Table 2-20 Section J.7: bearing on pins F/Ω = 15 ksi VII-16
From Part VI Beam Formulas Case 6 Simply supported beam, uniformly distributed load, R = W/2 = (1.2 k)/2 = 0.6 k A = (0.6 k)/(15 k/in2) = 0.04 in2, required bearing area The bearing area on the pin is the diameter of the pin times the length in bearing. D1 = A/(2t) = (0.04)/(2(0.080)) = 0.25 in. = diameter required, based on the bearing stress in the beam wall Determine the pin diameter based on bending of the pin. From Part V Table 4, the clearance between flanges of the 5 in. channel is: C = 5.00 - 2(0.26) = 4.48 in. Assuming the beam is at the bottom of the supporting channel, the lever arm for bending is the net clearance January 2010
plus half the wall thicknesses of the adjacent bearing surfaces. L = (4.48 - 4.00) + 0.080/2 + 0.26/2 = 0.65 in. A reasonable assumption to determine pin bending is that half of the connection load is transferred at the top of the beam. M = LR/2 = (0.65)(0.6/2) = 0.195 in-k The section modulus required is S = M/(F/Ω) = (0.195 in-k)/(25 k/in2) = 0.0078 in3,
January 2010
From Part V Table 28, for a round cross section S = πD3/32, which can be solved for D D = (32S/π)1/3 = ((32(0.0078)/π)1/3 = 0.43 in. This diameter is greater than the diameter based on bearing, therefore the required diameter is 0.43 in. Use a 7/16 in. diameter pin. NOTES: For cases in which the bearing load on a pin is toward the edge of the member, the allowable bearing should be reduced as required in Section J.7 of the Specification.
VII-17
Example 9 I BEAM IN AXIAL COMPRESSION Illustrating Sections E.1, E.3, E.4, and E.5 SOLUTION: From Part V Table 8 the section properties of an 8 in. × 6.18-lb/ft I-beam (I 8 × 6.18) are: A = 5.26 in2, rx = 3.37 in., d = 8.00 in., bf = 5.00 in., tf = 0.35 in., tw = 0.23 in. Chapter E addresses columns. Section E.1 requires that the allowable compressive strength is the least of the limit states of member buckling, local buckling, and the interaction between member buckling and local buckling, and establishes Wc = 1.65 for building structures. Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below. a) Member buckling is addressed in Section E.3. For flexural buckling, Section E.3.1 gives the slenderness as kL/r = (1)(8)(12)/3.37 = 28.5 < S2 = 66, so Fc /W = 20.3 - 0.127 (kL/r) = 20.3 - 0.127(28.5) = 16.7 ksi The member buckling stress is Fc = (16.7)(1.65) = 27.6 ksi The allowable axial compressive strength for member buckling is Pn = (F/W)Ag = (16.7)(5.26) = 87.8 k If in place of this doubly symmetric I-beam an unsymmetric open shape such as a channel, lipped angle, or hat shape were used, flexural-torsional buckling should be checked using Section E.3.2. b) Local buckling is addressed in Section E.4. Local buckling of the flange (a flat element with one edge supported) is addressed in Section B.5.4.1. The slenderness is
Figure 9 GIVEN: 1. Aluminum Association Standard I-beam I 8 × 6.18 2. Length: 8 ft 3. End conditions: pinned 4. Laterally supported to resist buckling about the weak axis 5. Alloy: 6061-T6 6. Structure type: building
REQUIRED:
b/t = (5.00 - 0.23)/(2 × 0.35) = 6.8 The slenderness is between S1 = 6.7 and S2 = 10.5, so Fc /W = 27.3 - 0.91(6.8) = 21.1 ksi The area of the flanges = Af = 2(5.00)(0.35) = 3.5 in2 Local buckling of the web (a flat element with both edges supported) is addressed in Section B.5.4.2. The slenderness is b/t = (8.00 - 2(0.35))/0.23 = 31.7
The allowable axial compressive strength. VII-18
January 2010
The slenderness is between S1 = 20.8 and S2 = 33, so Fc /W = 27.3 - 0.291(31.7) = 18.1 ksi
The elastic buckling stress of the web (a flat element with both edges supported) for the slenderness of 31.7 determined in b) above is
The area of the web = Aw = (8.00 - 2(0.35))(0.23) = 1.679 in2
p2( 10,100 ) p2E Fe= _______ = __________ = 38.7 ksi > 27.6 ksi 2 ( 1.6b/t ) ( 1.6( 31.7 ) )2
The weighted average allowable local buckling strength is Pn /W = (21.1)(3.5) + (18.1)(1.679) + (35/1.65) (5.26 - 3.5 - 1.679) = 106.0 k c) The interaction between member buckling and local buckling is addressed in Section E.5. Elastic buckling stresses are given in Section B.5.6.
= member buckling stress; therefore, the strength is not reduced by interaction between member and local buckling.
The allowable axial compressive strength is the lesser of 87.8 k and 106.0 k, which is 87.8 k.
The elastic buckling stress of the flange (a flat element with one edge supported) for the slenderness of 6.8 determined in b) above is p2( 10,100 ) p2E Fe= _______ = _________ = 86.2 ksi ( 5.0b/t )2 ( 5.0( 6.8 ) )2
January 2010
VII-19
Example 10 CORNER ANGLE OF A LATTICED BOX COLUMN Illustrating Sections E.1, E.3, E.4, and E.5 SOLUTION: From Part V, Table 14, the section properties of the 4 in. × 4 in. × 3/8 in. angle are A = 2.86 in.2, rx = ry = 1.22 in., rz = 0.766 in., lx = ly = 4.26 in4 The warping constant Cw = 0 for an angle. The torsional constant is J = (1/3)(0.375)3(4 + 3.625) = 0.134 in4 xo, yo = coordinates of the shear center with respect to the centroid xo = yo = 1.12 - 0.5(3/8) = 0.9325 in. Chapter E addresses columns. Section E.1 requires that the allowable compressive strength is the least of the limit states of member buckling, local buckling, and the interaction between member buckling and local buckling, and establishes Wc = 1.65 for building structures. Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below. a) Member buckling is addressed in Section E.3. Section E.3.2 addresses flexural-torsional buckling for unsymmetric shapes such as an angle. The elastic buckling stress Fe is the lowest root of the equation (Fe - Fex)(Fe - Fey)(Fe - Fez) - F e2(Fe - Fey)(xo/ro)2 - F e2(Fe - Fex)(yo/ro)2 = 0 where Ix+ Iy r 2o = x2o + y2o + _____ = 2(0.9325)2+ 2(4.26)/2.86 Ag = 4.72 in2
Figure 10
Fex= Fey= ______ π E 2 = π2(10,100)/(27/1.22)2= 203.5 ksi kxLx ____ rx 2
GIVEN: 1. Latticed box section column 2. Corner components: 4 in. × 4 in. × 3⁄8 in. angle 3. Alloy: 6061-T6 4. Spacing of lattice points: 27 in. o.c. 5. Connection of lattice: Riveted 6. Structure type: building
( )
(
)
(3/8)(10,100)(0.134) π2ECw ________________ Fez= ____ 1 2 GJ + ______ = (2.86)(4.72) Agro (kzLz)2
= 37.6 ksi
Solving for Fe by trial and error, Fe = 34.9 ksi. ___
______
√ F √ 34.9
REQUIRED:
10,100 (kL/re) = π __ E = π ______ = 53.4 < S 2= 66, so
Allowable axial compressive strength of a corner angle between lattice points.
Fc /W = 20.3 - 0.127(kL/r) = 20.3 - 0.127(53.4) = 13.5 ksi
VII-20
e
January 2010
The member buckling stress is Fc = (13.5)(1.65) = 22.3 ksi The allowable axial compressive strength for member buckling is Pn = (F/W)Ag = (13.5)(2.86) = 38.6 k b) Local buckling is addressed in Section E.4. Local buckling of the angle leg (a flat element with one edge supported) is addressed in Section B.5.4.1. The slenderness is b/t = (4.00 - 0.375)/0.375 = 9.7 The slenderness is between S1 = 6.7 and S2 = 10.5, so Fc /W = 27.3 - 0.91(9.7) = 18.5 ksi The allowable axial compressive strength for local buckling is Pn = (F/W)Ag = (18.5)(2.86) = 52.9 k c) The interaction between member buckling and local buckling is addressed in Section E.5. Elastic buckling stresses are given in Section B.5.6.
January 2010
The elastic buckling stress of the leg (a flat element with one edge supported) for the slenderness of 9.7 determined in b) above is p2( 10,100 ) p2E Fe= _______ = _________2 = 42.4 ksi > 22.3 ksi 2 ( 5.0b/t ) ( 5.0( 9.7 ) ) = member buckling stress; therefore, the strength is not reduced by interaction between member and local buckling. The allowable axial compressive strength is the lesser of 38.6 k and 52.9 k, which is 38.6 k. NOTES: The allowable axial compressive strength of the latticed column must also be determined for full length buckling resistance in accordance with Section E.3. The allowable strength is the lesser of this strength and four times the allowable strength of the corner angle computed above, whichever is smaller. The lattice diagonals brace the corner angles and must have adequate stiffness and strength to meet the requirements of Appendix 6.
VII-21
Example 11 WIDE FLANGE COLUMN Illustrating Sections E.1, E.3, E.4, and E.5 Chapter E addresses columns. Section E.1 requires that the allowable compressive strength is the least of the limit states of member buckling, local buckling, and the interaction between member buckling and local buckling, and establishes Wc = 1.65 for building structures. Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below. a) Member buckling is addressed in Section E.3. For flexural buckling, Section E.3.1 gives the slenderness as kL/r = (1)(42)/0.793 = 53.0 < S2 = 66, so Fc/W = 20.3 - 0.127(kL/r) = 20.3 - 0.127(53.0) = 13.6 ksi The member buckling stress is Fc = (13.6)(1.65) = 22.4 ksi The allowable axial compressive strength for member buckling is Pn = (F/W) Ag = (13.6)(2.60) = 35.4 k b) Local buckling is addressed in Section E.4. Local buckling of the flange (a flat element with one edge supported) is addressed in Section B.5.4.1. The slenderness is
Figure 11 GIVEN: 1. Column section: 4 in. × 3.50 in. × 3.06 lb/ft Army-Navy wide flange section. (WF (A-N) 4 × 3.06) 2. Length: 42 in. 3. End conditions: Pinned. 4. Alloy: 6061-T6. 5. Structure type: building
b/t = (3.50 - 0.25)/(2 × 0.25) = 6.5 < 6.7 = S1, so Fc/W = 21.2 ksi Local buckling of the web (a flat element with both edges supported) is addressed in Section B.5.4.2. The slenderness is b/t = (4.00 - 2(0.25))/0.25 = 14 < 20.8 = S1, so Fc/W = 21.2 ksi The weighted average allowable local buckling strength is Pn/W = (21.2)(2.60) = 55.1 k
REQUIRED: Allowable axial compressive strength.
SOLUTION: From Part V, Table 10, the section properties of WF (A-N) 4 × 3.06 are A = 2.60 in2, b = 3.50 in., t = 0.250 in., rx = 1.64 in., ry = 0.793 in. VII-22
c) The interaction between member buckling and local buckling is addressed in Section E.5. Elastic buckling stresses are given in Section B.5.6. The elastic buckling stress of the web (a flat element with both edges supported) for the slenderness of 14 determined in b) above is p2( 10,100 ) p2E Fe= _______ = _________2 = 199 ksi 2 ( 1.6b/t ) ( 1.6( 14 ) ) January 2010
The elastic buckling stress of the flange (a flat element with one edge supported) for the slenderness of 6.5 determined in b) above is p2( 10,100 ) p2E Fe= _______ = _________2 = 94.4 ksi > 22.4 ksi 2 ( 5.0b/t ) ( 5.0( 6.5 ) )
= member buckling stress; therefore, the strength is not reduced by interaction between member and local buckling.
The allowable axial compressive strength is the lesser of 35.4 k and 55.1 k, which is 35.4 k.
January 2010
VII-23
Example 12 SQUARE TUBE COLUMN Illustrating Sections E.1, E.3, E.4, and E.5 Chapter E addresses columns. Section E.1 requires that the allowable compressive strength is the least of the limit states of member buckling, local buckling, and the interaction between member buckling and local buckling, and establishes Wc = 1.65 for building structures. Allowable stresses for 3003-H14 given in Part VI Table 2-2 are used below. a) Member buckling is addressed in Section E.3. For flexural buckling, Section E.3.1 gives the slenderness as kL/r = (1)(48)/1.61 = 29.8 < S2 = 138, so Fc/W = 8.1 - 0.039 (kL/r) = 8.1 - 0.039(29.8) = 6.9 ksi The member buckling stress is Fc = (6.9)(1.65) = 11.4 ksi The allowable axial compressive strength for member buckling is Pn = (F/W) Ag = (6.9)(0.992) = 6.8 k
Figure 12 GIVEN: 1. 4 in. square tube column formed with lock-seam from 0.063 in. sheet. 2. Length: 48 in. 3. End conditions: Pinned. 4. Alloy: 3003-H14. 5. Structure type: building
REQUIRED:
SOLUTION: From Part V, Table 28, hollow square section properties are A = 42 - (4.00 - 0.063 × 2)2 = 0.992 in2 _______________
2+ (4 - 0.63(2))2 d 21 + d 22 4_______________ r = ______ = = 1.61 in. 12 12
√
√
NOTE: This method assumes sharp corners, whereas the actual corners of roll formed sections are rounded. Where the corner radius is small in comparison with the width of the section, this method is sufficiently accurate for practical purposes.
VII-24
Local buckling of a side (a flat element with both edges supported) is addressed in Section B.5.4.2. The slenderness is b/t = (4.00 - 2(0.063))/0.063 = 61.5 > 60 = S2, so Fc/W = 333/(61.5) = 5.4 ksi The weighted average allowable local buckling strength is Fc Ag/W = (5.4)(0.992) = 5.4 k
Allowable axial compressive strength.
_______
b) Local buckling is addressed in Section E.4.
c) The interaction between member buckling and local buckling is addressed in Section E.5. Elastic buckling stresses are given in Section B.5.6. The elastic buckling stress of a side (a flat element with both edges supported) for the slenderness of 61.5 determined in b) above is p2( 10,100 ) p2E Fe= _______ = __________ = 10.3 ksi < 11.4 ksi 2 ( 1.6b/t ) ( 1.6( 61.5 ) )2 = member buckling stress; therefore, the allowable strength cannot exceed:
(
)
(
)
1/3 F e2/3 Ag p2(10,100) 1/3 ___________ 10.32/3(0.992) p2E Pn /Ω = ______ _____ = _________ Ω 1.65 (kL/r)2 (29.8)2
= 13.8 k
The allowable axial compressive strength is the least of 6.8 k, 5.4 k, and 13.8 k, which is 5.4 k. January 2010
NOTES: The area of the lockseam is generally small and can be neglected. However, the seam must resist longitudinal slippage, otherwise the shape would be classed as an “open section” and would be subject to combined torsional and lateral buckling; see notes for Example 10.
January 2010
From Part VI, Table 3-1, 0.063 in. thick 3003-H14 is satisfactory for a zero bend radius. If the corner radii are large, they should be checked using Section B.5.4.5.
VII-25
Example 13 COLUMN WITH INTERMEDIATE STIFFENERS Illustrating Section B.5.4.4 The moment of inertia Io used in Section B.5.4.4 is of the area shown in the detail of Figure 13. The area width is 3.85 + 0.1 = 3.95 in. The element width b = 3.85 in. The element thickness t = 0.1 in. Properties As and Io are calculated from Part V, Table 28: In = bn dn3/12, where bn is the width and dn is the height An = area of an element Yn = vertical distance from bottom fiber to the centroid of the element n 1 2
bn dn 3.95 0.1 0.1 1.0 Totals
An Yn AYn AY 2n In 0.395 1.05 0.4147 0.4355 0.0003 0.1 0.5 0.05 0.025 0.0083 0.495 0.4647 0.4605 0.0086
ΣA Yn ______ c = ______ n = 0.4647 = 0.9389 in. ΣAn 0.495 Io = ∑(AnY 2n ) - c2∑An + ∑In
Figure 13
GIVEN: 1. An 8 in. square tube column, with 0.10 in. thick walls and 0.10 in. thick by 1 in. long stiffeners at the middle of each side. 2. Alloy: 6061-T6 extrusion. 3. Structure type: building
REQUIRED: Allowable local buckling compressive stress.
Io = 0.4605 - (0.9389)2 (0.495) + (0.0086) = 0.03275 _____________________
√
( )( ) 1 + _________ 1.0 0.1 ( ) ( ) 3.85 0.1 3.85 ________________ λs= ( 4.62 )____ _____________________ 0.1 ) 10.67( 0.03275 1 + 1 + _____________ 3 3.85( 0.1 )
√
λs = 61.4 < 66 = S2 F1/W = 23.9 - 0.149 (61.4) = 14.8 ksi Check the flat elements on either side of the stiffener: b/t = ____ 3.85 = 38.5 > 33 = S2 0.1
SOLUTION:
from Section B.5.4.2
Section B.5.4.4 addresses uniform compression of flat elements supported on both edges and with an intermediate stiffener.
F2/W = 580/38.5 = 15.1 ksi > 14.8 ksi = F1
VII-26
So Fc/W = F1/W = 14.8 ksi
January 2010
Example 14 ROUND TUBE COLUMN Illustrating Sections E.1, E.3, and E.4 REQUIRED: The wall thickness of a standard tube that has an allowable axial compressive strength of at least 40 k.
SOLUTION: From Part V, Table 21, round tubes, the radius of gyration r of 6 in. OD tubes ranges from 1.80 in. to 2.08 in.. Select from the table the trial wall thickness of 0.188 in. for which A = 3.43 in2 and r = 2.06 in.. Chapter E addresses columns. Section E.1 establishes Wc = 1.65 for building structures. Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below. a) Member buckling is addressed in Section E.3. For flexural buckling, Section E.3.1 gives the slenderness as kL/r = (1)(18)/2.06 = 8.7 < S2 = 66, so Fc/W = 20.3 - 0.127 (kL/r) = 20.3 - 0.127(8.7) = 19.2 ksi The allowable axial compressive strength for member buckling is (F/W) Ag = (19.2)(3.43) = 65.8 k > 40 k b) Local buckling is addressed in Section E.4. Local buckling of a curved element supported on both edges is addressed in Section B.5.4.5. The slenderness is Rb/t = (6.0 - 0.188)/2/0.188 = 15.5 < 27.6 = S1, so Fc/W = 21.2 ksi
Figure 14 GIVEN: 1. Shape: Round tube, 6 in. OD (outside diameter). 2. Load: 40 k (40,000 lb), concentric. 3. Length: 18 in. 4. Alloy: 6061-T6. 5. End Conditions: pinned. 6. Structure type: building
January 2010
The weighted average allowable local buckling strength is AgFc /W = (21.2)(3.43) = 72.7 k > 40 k The wall thickness t = 0.188 in. is satisfactory.
VII-27
Example 15 I-BEAM IN BENDING Illustrating Sections F.2, F.8, and G.2
Figure 15 GIVEN: 1. Section: Aluminum Association Standard I-beam I5 × 3.70 2. Beam length: 16 ft. with lateral supports at vertical supports only. 3. Vertical support spacing 4 ft. o.c. (first support at end of beam). 4. Alloy: 6061-T6. 5. Structure type: building
REQUIRED: Allowable uniform load that can be applied to the bottom flange.
SOLUTION: Part V, Table 8, gives the section properties:
a) Section F.2.1 addresses lateral-torsional buckling. To
L determine the slenderness ratio ______ b___ , Section F.1.1 ry √ Cb
allows the bending coefficient Cb to be conservatively taken as 1. L 48 __ r b = _____ = 56.3 < S2= 79, so y
0.853
L Fb/Ω = 23.9 - 0.124 __ ryb Fb/Ω = 23.9 - 0.124 (56.3) = 16.9 ksi The lateral-torsional buckling stress Fb = (1.65)(16.9 ksi) = 27.9 ksi b) Section F.2.3 addresses interaction between local buckling and lateral-torsional buckling.
Sx = 5.58 in3, b = 3.5 in., tw = 0.19 in., tf = 0.32 in., ry = 0.853 in., Iy = 2.29 in4, J = 0.0984 in4
The flange’s elastic buckling stress given in Section B.5.6 is
The flange’s slenderness ratio is b/t = (3.5 - 0.19)/2/0.32 = 5.2
p2( 10,000 ) p2E Fe= _______ = _________2 = 147 ksi > 27.9 ksi 2 ( 5.0b/t ) ( 5.0( 5.2 ) )
The web’s slenderness ratio is b/t = (5.0 - 2(0.32))/0.19 = 22.9
Because the flange’s elastic buckling stress is not less than the beam’s lateral-torsional buckling stress, the beam’s flexural capacity is not limited by the interaction between local buckling and lateral-torsional buckling.
Section F.1 establishes safety factors of 1.95 on tensile rupture and 1.65 on all other limit states for flexure of building-type structures. Section F.2 requires that Sections F.2.1, F.2.3, and F.8 be used to determine the flexural strength of open shapes. Section G.2 addresses the shear strength of flat webs. Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below.
VII-28
c) Section F.8 addresses elements of flexural members. 1) Section F.8.1 addresses tension. Section F.8.1.1 addresses elements in uniform tension (the flange), for which Fb /W = 19.5 ksi, Section F.8.1.2 addresses elements in flexure (the web), for which Fb /W = 27.6 ksi.
January 2010
2) Section F.8.2 addresses compression. Section B.5.4.1 addresses the flange; b/t = 5.2 < 6.7 = S1, so Fb /W = 21.2 ksi Section B.5.5.1 addresses the web; b/t = 22.9 < 49.3 = S1, so Fb /W = 27.6 ksi The least of these allowable stresses is for lateraltorsional buckling; therefore, Fb /W = 16.9 ksi and the allowable moment is M = FSx = 16.9(5.58) = 94.3 in-k. From Part VI Beam Formulas Case 43, continuous beam of four equal spans with a uniformly distributed load, the maximum bending moment is 2 168wL M = -_______ 1568
Rewriting to solve for w, ( ) w = ______ 1568M = __________ 1568 94.3 = 0.382 k/in.
1 68L2 168( 48 )2 = allowable distributed load for flexure The section is symmetrical about its X axis; therefore, the allowable positive moment is equal to the allowable negative moment. Thus, the minus sign for w may be removed. d) Section G.2 addresses web shear b/t = 22.9 < S1 = 35.3, so Fs/W = 12.7 ksi A = dtw = (5.00)(0.19) = 0.95 in2 = area of web V = AFs/W = 0.95(12.7) = 12.1 k, allowable shear
January 2010
From Part VI Beam Formulas Case 43, the maximum shear is V = _____ 17wL , which can be written 28 w = ____ 28V , which w is unknown 17L ( ) w = ________ 28 12.1 = 0.415 k/in. = allowable distributed load 17( 48 ) for shear
Using the smaller of the loads for flexure and shear, the allowable uniform load is 0.382 k/in. NOTES: Example 3 notes also apply to this example. A more accurate flexural strength can be determined by using Section F.2.2 to compute rye. For shapes symmetric about the bending axis and where the load acts downward on the bottom flange (away from the beam’s shear center), Section F.2.2.1 gives: _______________________________________ _____________________________ _______________________
√
√[ √
( 5.00 ) ]
) 2.29( 5.00 0.0984 48 2 ______ rye = ___ 1 _________ 0.5 + 1.25 + 0.152 ____
1.7
5.58
2.29
= 0.984 in. rye may be used in place of ry = 0.853 in. to compute the lateral-torsional buckling strength.
VII-29
Example 16 WELDED GIRDER IN BENDING Illustrating Sections F.2, F.8, F.9 The height of the centroid of the section
ΣA Yn _____ ct= ______ n = 1248 = 27.1 in. ΣAn 46.0 Ix = ∑(AnY 2n ) - c 2t ∑An + ∑In = 20,132 in4 For the compression flange, cc = 50.0 - 27.1 = 22.9 in. The section modulus for compression is Sc = Ix /cc = 20,132/22.9 = 879 in3 The section modulus for tension is St = Ix /ct = 20,132/27.1 = 743 in3
Figure 16 GIVEN: 1. Welded girder, see Figure 16 2. Lateral support spacing: compression flange, 10 ft o.c. 3. Alloy: 5456-H321 4. Structure type: bridge 5. Number of load cycles: 500,000
REQUIRED:
Section F.2.2.2 addresses flexure of singly symmetric shapes unsymmetric about the bending axis and allows computing ry by treating both tension and compression flanges identical to the compression flange of the actual section. To compute the area and the moment of inertia about the Y axis of such a section: n 1 2 3
bn 1.0 48.0 1.0 Totals
dn 16.0 0.375 16.0
Allowable bending moment with the top flange in compression.
Iy = ∑In = 682 in4
SOLUTION:
Iy ry= __ = ____ 682 = 3.69 in. Ay 50
In = bn dn3/12 where bn is the width, and dn, is the height. An = area of an element Yn = vertical distance from bottom fiber to centroid of element
VII-30
In 341 0 341 682
Ay = 50.0 in2
____
√ √
To compute section properties, see Part V, Table 28. The moment of inertia of a rectangle about its centroid is
n bn dn 1 16.0 1.00 2 0.375 48.0 3 12.0 1.00 Totals
___
An 16.0 18.0 16.0 50.0
An 16.0 18.0 12.0 46.0
Yn 49.5 25.0 0.5
AYn AY 2n In 792 39204 1 450 11250 3456 6 3 1 1248 50457 3458
For the portion of the cross section outside the weldaffected zone, Table A.3.4 gives mechanical properties for 5456-H321 plate. The web is 3⁄8 in. thick plate (with Ftu = 46 ksi) and the flange is 1 in. thick plate (with Ftu = 44 ksi). For design, conservatively use the mechanical properties of the flange throughout the section: E = 10,400 ksi, Ftu = 44 ksi, Fty = 31 ksi, Fcy = 25 ksi From Part VI, Table 1-1, the buckling constants for the unwelded material are Bc = 29.0
Bp = 34.6
Bbr = 46.1
Dc = 0.187
Dp = 0.245
Dbr = 0.376
Cc = 103
Cp = 94
Cbr = 82 January 2010
From Table B.4.3, k1 = 0.50, k2 = 2.04 For the portion of the cross section in the weld-affected zone, Table A.3.5 gives mechanical properties for 5456H321 plate: E = 10,400 ksi, Ftu = 42 ksi, Fty = 19 ksi, Fcy = 19 ksi From Part VI, Table 1-2, the buckling constants for the weld affected material are
Mn/Ω = 11,370(1 - 2.75/18.5) + 8,710(2.75/18.5) = 10,970 in-k The lateral-torsional buckling stress Fb = W Mn/Sc Fb = (1.85)(10,970 in-k/879 in3) = 23.1 k/in2 b) Section F.2.3 addresses interaction between local buckling and lateral-torsional buckling. The flange’s slenderness ratio is
Bc = 21.6
Bp = 25.7
Bbr = 34.1
b/t = (16 - 0.375)/2/1 = 7.8
Dc = 0.121
Dp = 0.156
Dbr = 0.240
Cc = 119
Cp = 110
Cbr = 95
The flange’s elastic buckling stress given in Section B.5.6 is
From Table B.4.3, k1 = 0.50, k2 = 2.04 Section F.1 establishes safety factors of 2.20 on tensile rupture and 1.85 on all other limit states for flexure of bridgetype structures. Section F.2 requires that Sections F.2.1, F.2.3, and F.8 be used to determine the flexural strength of open shapes subject to lateral-torsional buckling.
p2( 10,400 ) p2E Fe= _______ = _________ = 67.5 ksi > 23.1 ksi ( 5.0b/t )2 ( 5.0( 7.8 ) )2 Because the flange’s elastic buckling stress is not less than the beam’s lateral-torsional buckling stress, the beam’s flexural capacity is not limited by the interaction between local buckling and lateral-torsional buckling.
For a beam with no portion weld-affected:
c) Section F.8 addresses elements of flexural members. 1) Section F.8.1 addresses tension. Section F.8.1.1 addresses elements in uniform tension (the flange). The weld affected area of the tension flange is Awz = 2.375(1) = 2.375 in2 The gross area of the tension flange is Awz = 12(1) = 12 in2
L 120 __ r b = ____ = 32.5 122 = S2, ____
k B E mb/t
____________
2.04√ ( 34.1 )( 10,400 ) √ so F bo= _______ 2 br = _________________ = 16.4 ksi ( 0.58 )( 128 )
Fbw/W = 16.4/1.85 = 8.8 ksi Section B.5.5 provides the strength of the web in compression as Fb = Fbo (1 - Awzc /Agc) + Fbw Awzc /Agc The gross area of the web in compression is Ag = 0.375(22.9 - 1) = 8.21 in2 The weld-affected area of the web in compression is Awz = (1)(0.375) = 0.375 in2 Fb /W = [Fbo (1 - Awzc /Agc) + FbwAwzc /Agc ]/W Fb /W = [10.3(1 - 0.375/8.21) + 8.8(0.375)/8.21] = 10.2 ksi Section F.8.3 provides the weighted average strength of the elements. The moment of inertia of the flanges is If = (12)(1)3/12 + (16)(1)3/12 + (16)(1)(22.9 - 0.5)2 + (12)(1)(27.1 - 0.5)2 = 16,521 in4 The moment of inertia of the web is Iw = (0.375)(48)3/12 + (0.375)(48)(27.1 - 25)2 = 3535 in4 For compression, Mnc = Fcf If /ccf + Fcw Iw /ccw Mnc/W = (13.0)(16521)/(22.9 - 0.5) + (10.2)(3535)/22.9 - 1) = 11,235 in-k. January 2010
For tension, Mnt = Ftf If /ctf + Ftw Iw /ctw Mnt /W = (15.5)(16521)/(27.1) + (21.5)(3535)/27.1 - 1) = 12,360 in-k. The allowable moments are: For lateral-torsional buckling: Mn/W =10,970 in-k For local buckling: Mn/W =11,235 in-k For tension: Mn/W =12,360 in-k The least of these is 10,970 in-k from lateral torsional buckling. Allowable moment based on fatigue per Appendix 3 Figure 3.1 detail 4 is similar to this example. Table 3.1 indicates that this detail is fatigue category B. Section 3.2 requires that for constant amplitude loading the applied stress range Sra be less than the allowable stress range Srd: Sra < Srd = Cf N-1/m For category B, Table 3.2 gives Cf = 130 ksi and m = 4.84, so Srd = (130 ksi)/(500,000)1/4.84 = 8.6 ksi Assuming that the dead load stresses are negligible, the maximum stress equals the stress range. The section modulus corresponding to the weld on the tension flange is Sw = 20,132/(27.1 - 1.0) = 771 in3
January 2010
The tensile moment for fatigue Mf for the tensile stress range is Mf = Srd Sw = (8.6 k/in2)(771 in3) = 6630 in-k If variable amplitude loading occurred, an equivalent stress range would be calculated to compare to the allowable stress range. For example, if the loading were 100,000 cycles 50,000 cycles 350,000 cycles 500,000 cycles
9.5 ksi stress range 10.0 ksi stress range 7.1 ksi stress range at various stress ranges
Section 3.3 provides the equivalent stress range Sre for variable amplitude loading: Sre = [(100/500)9.54.84 + (50/500)10.04.84 + (350/500)7.14.84]1/4.84 = 8.2 ksi < 8.6 ksi So this variable amplitude loading does not exceed the allowable stress range. Selection of allowable moment Comparing the allowable static (10,970 in-k) and fatigue (6630 in-k) moments, the allowable moment is 6630 in-k from fatigue. NOTES: If the shape of the moment diagram is known the lateral-torsional buckling strength could be determined more precisely by using the larger, more accurate value of rye, computed according to Section F.2.2.
VII-33
Example 17 WELDED BEAM SUBJECT TO FATIGUE Illustrating Sections 3.1 and 3.2
(a)
(b)
Figure 17 GIVEN: Same as Example 16 except that the number of load cycles = 500,000.
REQUIRED: Allowable bending moment range for fatigue loading of the beams shown in Figure 17.
The section modulus, Sw corresponding to the weld location on the tension flange is: Sw = 20,132/(27.1-1.0) = 771 in3 The allowable moment range for fatigue DM is calculated for a tensile stress range at the web. DM = SrdSw = 8.6 (771) = 6630 in-k
SOLUTION: a) Beam with no transverse brackets Specification Figure 3.1 Example 4 is a girder with continuous welds attaching web and flange, similar to that shown in Figure 17a. The stress category is selected from Table 3.1. The category for a built-up member (see general condition in left column) with continuous weld parallel to the direction of stress for example numbers 3, 4, and 5 (right column) is B. Section 3.2 requires for constant amplitude loading that the applied stress range Sra shall not exceed the allowable stress range Srd
If variable amplitude loading occurred, an equivalent stress range would be calculated and compared to the allowable stress range. For example, if the loading were
100,000 cycles 9.5 ksi stress range 50,000 cycles 10.0 ksi stress range 350,000 cycles 7.1 ksi stress range 500,000 cycles at various stress ranges
Section 3.3 requires that the equivalent stress range Sre shall not exceed the allowable stress range Srd
Srd = Cf N-1/m Where, for Stress Category B, Cf = 130 ksi and m = 4.84 for the number of cycles, N = 500,000, Srd = (130)(500,000)-1/4.84 = 8.6 ksi VII-34
Sre = [(100/500)9.54.84 + (50/500)104.84 + (350/500)7.14.84]1/4.84 Sre = 8.2 ksi < 8.6 ksi = Srd So this variable amplitude loading does not exceed the allowable stress range. January 2010
b) Beam with transverse brackets Specification Figure 3.1 Example 6 is a girder with a similar detail at the bottom of the stiffener to that shown in Figure 17b. The category corresponding to Example 6 is C. Section 3.2 requires for constant amplitude loading that the applied stress range Sra shall not exceed the allowable stress range Srd
for the number of cycles, N = 500,000, Srd = (278)(500,000)-1/3.64 = 7.6 ksi The section modulus at the bottom end of the stiffener is: Sw = (20,132)/(27.1 - 4.0) = 872 in3 The allowable moment range for fatigue DM is calculated for a tensile stress range at the end of the stiffener.
Srd = Cf N-1/m Where, for stress category C,
DM = (7.6 k/in2)(872 in3) = 6630 in-k
Cf = 278 ksi and m = 3.64
January 2010
VII-35
Example 18 PIPE IN BENDING Illustrating Section F.6
Figure 18 GIVEN:
For the limit state of tensile rupture, the allowable stress is
1. Concentrated load of 5.5 k (5,500 lb) at mid-span. 2. Span: 10 ft, simply supported. 3. Alloy: 6061-T6. 4. Structure type: building
1.24Ftu /[(1.95)(kt)] = 1.24(38)/1.95/1.0 = 24.2 ksi
REQUIRED: Wall thickness of thinnest 6 in. pipe with an allowable load that exceeds the concentrated load.
SOLUTION: Section F.1 establishes safety factors of 1.95 on tensile rupture and 1.65 on all other limit states for flexure of building-type structures. Section F.6 addresses round tubes in flexure. Allowable stresses for 6061-T6 are given in Part VI Table 2-19 are used below. Section F.6.1 addresses the limit states of yielding and rupture. For the limit state of compressive yielding, the allowable stress is 1.17Fty /1.65 = 1.17(35)/1.65 = 24.8 ksi
From Part VI Beam Formulas Case 1, a simply supported beam with a concentrated load P at center, the maximum moment is M = PL/4 = (5.5)(10)(12)/4 = 165 in-k S = M/(F/Ω) = (165 in-k)/(24.4 ksi) = 6.82 in3, trial section modulus Part V Table 22 shows that a 6.625 in. OD Schedule 40 pipe with a wall thickness of 0.280 in. and section modulus of 8.50 in3 is the thinnest 6 in. pipe with a section modulus greater than 6.82 in3. Rb /t = (6.625 - 0.280)/2/0.280 = 11.3 < 55 = S1 So Fb /Ω = 39.3 - 2.702(Rb /t)1/2 = 30.2 ksi > 24.2 ksi The trial beam is therefore satisfactory; use Schedule 40 pipe.
For the limit state of tensile yielding, the allowable stress is 1.17Fty /1.65 = 1.17(35)/1.65 = 24.8 ksi
VII-36
January 2010
Example 19 RECTANGULAR BAR IN BENDING Illustrating Section F.4
Figure 19 GIVEN: 1. Beam section: 1.50 in. deep rectangular bar. 2. Load 0.500 k (500 lb) at mid-span. 3. Span: 36 in. 4. Ends of beam restrained against rotation and translation, lateral support at ends only. 5. Alloy: 5052-H34. 6. Structure type: building
REQUIRED: The thinnest standard bar with an allowable load that exceeds the applied load.
SOLUTION: From Part V Table 28 provides section properties for a rectangle Try a 1/4 in. thick bar A = 0.25 (1.50) = 0.375 in2 Ix = (0.25)(1.5)3/12 = 0.070 in4 Since this section is symmetric about the x-axis, c = d/2 = 1.5/2 = 0.75 in. From Part VI, Beam Formulas Case 26, concentrated load P at center, the maximum moment is M = PL/8 = (0.5)(36)/8 = 2.25 in-k
Section F.1 establishes safety factors of 1.95 on tensile rupture and 1.65 on all other limit states for flexure of building-type structures. Section F.4 addresses flexure of solid rectangular shapes. Part VI Table 2-10 gives allowable stresses for 5052-H34. Section F.4.1 addresses the limit states of yielding and rupture: For the limit state of compressive yielding, the allowable stress is 1.3Fcy /1.65 = 1.3(24)/1.65 = 18.9 ksi For the limit state of tensile yielding, the allowable stress is 1.3Fty /1.65 = 1.3(26)/1.65 = 20.5 ksi For the limit state of tensile rupture, the allowable stress is 1.42Ftu /[(1.95)(kt)] = 1.42(34)/1.95/1.0 = 24.8 ksi Since the least of these allowable stresses is 18.9 ksi < 24.1 ksi, a thicker bar is needed. Try a 3/8 in. thick bar A = 0.563 in2 Ix = 0.105 in4 f = Mc/I = (2.25)(0.75)/(0.105) = 16 ksi < 18.9 ksi
The flexural stress at the extreme fiber is f = Mc/I = (2.25)(0.75)/(0.070) = 24.1 ksi
January 2010
VII-37
Now check the limit state of lateral-torsional buckling addressed in Section F.4.2. Conservatively using Cb = 1.0, ____
_______
t Cbd
0.375 (1)(1.5)
√
L S = __ d ____ b = _____ 1.5 _______ 36 = 19.6 < S2= 36
√
F/Ω = 26.7 - 0.495(19.6) = 17.0 ksi
VII-38
The section modulus of a 5⁄16 in. wide bar would be 5⁄6 of the section modulus of a 3⁄8 in. wide bar. Since the stress f = 16 ksi is more than 5⁄6 of the allowable of 17.0 ksi, a 5⁄16 in. bar will not be satisfy the requirements even at the stress permitted for a 3⁄8 in. bar. Use a 3⁄8 in. thick bar.
January 2010
Example 20 RECTANGULAR TUBE IN BENDING Illustrating Sections F.3 and F.8
Figure 20 GIVEN: 1. 4 in. × 2 in rectangular tube with 0.188 in. wall (RT 2 × 4 × 0.188) 2. Load: 20 lb/ft2 total live and dead loads. 3. 12 ft simple span, laterally unsupported. 4. Alloy: 6063-T5. 5. Structure type: building
REQUIRED: The maximum allowable spacing of the beams.
SOLUTION: Part V Table 24 provides section properties for rectangular tubes: Ix = 4.23 in4, Sx = 2.11 in3, Iy = 1.37 in4, J = 3.19 in4 The slenderness ratio of the flange is b/t = (2 - 2(0.188))/0.188 = 8.6 The slenderness ratio of the web is b/t = (4 - 2(0.188))/0.188 = 19.3 Section F.1 establishes safety factors of 1.95 on tensile rupture and 1.65 on all other limit states for flexure of building-type structures. Section F.3 addresses flexure of tubular shapes. Because the tubes are bent about their major axis, they are subject to lateral-torsional buckling and must meet the requirements of both Section F.3 and F.8. Part VI Table 2-20 gives allowable stresses for 6063-T5. Section F.8.1 addresses tension. Section F.8.1.1 addresses elements in uniform tension (the flange), for which Fb/W = 9.7 ksi, Section F.8.1.2 addresses elements in flexure (the web), for which Fb/W = 12.6 ksi. January 2010
Conservatively use the lesser of these in lieu of the weighted average tensile strength given in Section F.8.3. Section F.8.2 addresses compression. Section B.5.4.2 addresses the flange; b/t = 8.6 < 25.6 = S1, so Fb /W = 9.7 ksi Section B.5.5.1 addresses the web; b/t = 19.3 < 62.9 = S1, so Fb /W = 12.6 ksi Conservatively use the lesser of these in lieu of the weighted average compressive strength given in Section F.8.3. Section F.3.1 addresses lateral-torsional buckling. Conservatively using Cb = 1.0, 2L Sc ___________ ( 144 )( 2.11 ) S = ______ b___ = 2_________ = 291 < S2= 3823 Cb√IyJ √ 1.37( 3.19 ) Fb/W = 10.5 - 0.070(291)1/2 = 9.3 ksi The lowest allowable stress is 9.3 ksi M = ScFb/W = 2.11(9.3) = 19.6 in-k Part V Beam Formulas Case 6, simply supported beam with uniform load, has a maximum moment of M = WL/8, which can be written as W = 8M/L W1 = 8(19.6)/144 = 1.09 k = allowable total load for flexure Section G.2 addresses web shear b/t = (4 - 2(0.188))/0.188 = 19.3 < S1 = 43.6 Fs /W = 5.8 ksi VII-39
Web area A = 2 × 0.188 × 4 = 1.5 in2 V = (Fs /Ω) A = 5.8 × 1.5 = 8.7 k W2 = 2V = 2 × 8.7 = 17.4 k = allowable load for shear.
The allowable spacing can now be determined from the given unit load of 20 lb/ft2 or 0.020 k/ft2 Spacing = (1.09 k)/[0.020 k/ft2)(12 ft)] = 4.54 ft o.c. = 54 in. The center to center spacing of the beams should therefore not exceed 54 in.
Since W1 < W2, lateral-torsional buckling controls W = W1 = 1.09 k, the total allowable load per beam.
VII-40
January 2010
Example 21 I-BEAM IN BENDING Illustrating Section F.8
Figure 21
GIVEN: 1. Uniform load: 1.0 k/ft (1,000 lb/ft) including dead load. 2. Span: 18 ft, simply supported. 3. Compression flange is adequately supported laterally. 4. Alloy: 6061-T6. 5. Structure type: building
REQUIRED: Size of lightest Aluminum Association standard I-beam with an allowable load that exceeds 1.0 k/ft.
SOLUTION: Part VI Beam Formulas Case 6 gives the total load W as W = wL = 1.0 × 18.0 = 18.0 k Part VI Table 4-2 indicates that an I 10 × 8.65 will support 19.69 k at a 17 ft span; therefore, it may be the desired beam. The allowable load for an 18 ft span is not tabulated, but it can be determined as follows: Maximum bending moment, M = WL/8 = (18 k)(18 ft)(12 in/ft)/8 = 486 in-k Part V, Table 8, gives the section properties: Sx = 26.4 in3, b = 6 in., tw = 0.25 in., tf = 0.41 in. January 2010
The flange’s slenderness ratio is b/t = (6 - 0.25)/2/0.41 = 7.0 The web’s slenderness ratio is b/t = (10.0 - 2(0.41))/0.25 = 36.7 Section F.1 establishes safety factors of 1.95 on tensile rupture and 1.65 on all other limit states for flexure of building-type structures. Because the compression flange is laterally supported, the beam is not subject to lateraltorsional buckling. For open shapes not subject to lateraltorsional buckling, Section F.2 requires that Section F.8 be used to determine the flexural strength. Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below. Section F.8 addresses elements of flexural members. a) Section F.8.1 addresses tension. Section F.8.1.1 addresses elements in uniform tension (the flange), for which Fb /W = 19.5 ksi, Section F.8.1.2 addresses elements in flexure (the web), for which Fb /W = 27.6 ksi. b) Section F.8.2 addresses compression. Section B.5.4.1 addresses the flange; b/t = 7.0 > 6.7 = S1, so Fb /W = 27.3 - 0.91(7.0) = 20.9 ksi VII-41
Section B.5.5.1 addresses the web; b/t = 36.7 < 49.3 = S1, so Fb /W = 27.6 ksi The least of these allowable stresses is 19.5 ksi. f = M/S = 486/(26.4) = 18.4 k/in2 < 19.5 ksi
VII-42
Since the calculated stress, 18.4 ksi, is less than the allowable tensile stress of 19.5 ksi and the allowable compressive stress of 20.9 ksi, the trial beam is satisfactory. NOTE: Section G.2 should be also be checked. It will be more likely to govern for short, heavily loaded beams.
January 2010
Example 22 UNSYMMETRIC BEAM IN BENDING Illustrating Sections B.5.4.1, B.5.4.2, B.5.4.3, B.5.5.1, and F.8 The allowable moment for tension is M1 = FI/ct = (19.5)(5.15)/3.70 = 27.1 in-k Section F.8.1.2 addresses elements in flexure (the web), for which Fb /W = 27.6 ksi. Conservatively use the lesser of the allowable tensile stresses for the web and flange. b) Section F.8.2 addresses compression. Section B.5.5.1 addresses elements in flexure (the web). The web slenderness is b/t = (6 - 2(0.072))/0.072 = 81.3 cc = -(6 - 3.7) = -2.3; co = 3.7 co/cc = 3.7/(-2.3) = -1.6 < -1, so m = 1.3/(1 - co/cc) = 1.3/(1 - (3.7/-2.3)) = 0.50
Figure 22
S2 = k1Bbr /(mDbr) = 0.5(66.8)/[(0.5)(0.665)] = 100.5
GIVEN: 1. Beam of cross section shown in Figure 22 2. Continuous lateral support of compression (top) flange 3. Alloy: 6061-T6 4. Structure type: building
Allowable bending moment.
SOLUTION: The section properties are computed as shown in example 16 with the following results: Ix = 5.15 in4
Section F.1 establishes safety factors of 1.95 on tensile rupture and 1.65 on all other limit states for flexure of building-type structures. Because the compression flange is laterally supported, the beam is not subject to lateraltorsional buckling. For open shapes not subject to lateraltorsional buckling, Section F.2 requires that Section F.8 be used to determine the flexural strength. Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below. Section F.8 addresses elements of flexural members. a) Section F.8.1 addresses tension. Section F.8.1.1 addresses elements in uniform tension (the flange), for which Fb W = 19.5 ksi, January 2010
Since S1 = 64.1 < 81.3 < 100.5 = S2, Fb/Ω = [Bbr - mDbr(b/t)]/ Ω = (66.8 - 0.5(0.665)(81.3))/1.65 = 24.1 ksi The allowable moment based on web compression is
REQUIRED:
ct = 3.70 in.
S1 = (Bbr - 1.3Fcy)/(mDbr) = (66.8 - 1.3(35))/(0.5(0.665) = 64.1
M2 = (24.1)(5.15)/(6 - 3.70 - 0.072) = 55.7 in-k The distance from the neutral axis to the centroid of the flange stiffener is c = 6 - 3.70 - 0.072 - 0.5(0.7 - 0.072) = 1.91 in. The stiffener can be treated as an element in uniform compression if the distance from the neutral axis to the centroid of the stiffener is greater than 75% of the distance from the neutral axis to the extreme fiber. The distance from the neutral axis to the extreme fiber c = 6 - 3.70 = 2.3 in.; 0.75(2.3) = 1.72 in. < 1.91 in., so treat the stiffener as an element in uniform compression. Section B.5.4.1 addresses elements in uniform compression supported on one edge. The stiffener’s slenderness is b/t = (0.70 - 0.072)/0.072 = 8.7, which is between 6.7 = S1 and 10.5 = S2, so Fb/W = 27.3 - 0.91(8.7) = 19.4 ksi The allowable moment based on stiffener compression is M3 = (19.4)(5.15)/(6 - 3.70 - 0.072) = 44.8 in-k VII-43
Section B.5.4.3 addresses elements supported on one edge and with a stiffener at the other edge. The flange element width is b = (4 - 3(0.072))/2 = 1.89 in. The depth of the stiffener is Ds = 0.70 - 0.072 = 0.628 in. Ds/b = 0.628/1.89 = 0.33 < 0.8, so Section B.5.4.3 applies. ______
___
√
Fc /W = 7.1 + (19.7 - 7.1) (0.797) = 17.1 ksi
2Se = 43.5 > 26.25 = b/t > 21.7 = Se, so r s 0.363 rst= __________ = __________________ 26.25 + 3 b/t ___ 1.5t + 3 1.5( 0.072 ) _____ 21.7 Se
(
)
= 0.797 ≤ 1.0 FUT /W = allowable stress for flange as if supported on one edge per B.5.4.1
VII-44
S1 = 20.8 < b/t = 26.25 < 33 = S2
Fc /W = FUT /W + (FST /W - FUT /W)rST ≤ FST
d sinθ 0.7 - __ 0.072 rs= _____ s __ = __________ = 0.363 √ √ 3 3
)
FST /W = allowable stress for flange as supported on both edges per B.5.4.2
FST /W = 19.7 ksi
b/t = 1.89/0.072 = 26.25
(
FUT /W = 186/26.25 = 7.1 ksi
FST /W = 27.3 - 0.291 (b/t) = 27.3 - 0.291(26.25)
10,100 Se= 1.28 ___ E = 1.28 ______ = 21.7 Fcy 35
√
b/t = 26.25 > 10.5 = S2, so
M4 = (17.1)(5.15)/(6 - 3.70 - (0.072/2)) = 38.9 in-k The smallest of the allowable moments M1 thru M4 is M1, so the allowable moment is M = 27.1 in-k NOTE: Shear stress would be checked using Section G.2.
January 2010
Example 23 CHANNEL IN BENDING Illustrating Sections B.5.4.1, B.5.5.1, B.5.5.2, and F.8
Figure 23 GIVEN: 1. 2.5 in. × 2 in. × 0.125 in. channels as shown in Figure 23 2. Alloy: 6063-T6 3. Structure type: building
REQUIRED: The allowable positive bending moment about the X-X axis for each channel shown in Figure 23
SOLUTION: Part I, channel without stiffener lips: The section properties are computed using the method shown in example 16 with the following results: c = 1.34 in. to the top fiber I = 0.325 in4 Section F.1 establishes safety factors of 1.95 on tensile rupture and 1.65 on all other limit states for flexure of building-type structures. Because the channel is bent about its weak axis, it is not subject to lateral-torsional buckling. For open shapes not subject to lateral-torsional buckling, Section F.2 requires that Section F.8 be used to determine the flexural strength. Allowable stresses for 6063-T6 given in Part VI Table 2-21 are used below. Section F.8 addresses elements of flexural members. a) Section F.8.1 addresses tension. Section F.8.1.1 addresses elements in uniform tension (the flange), for which Fb/W = 15.2 ksi,
January 2010
The allowable moment for tension in the flange is M1 = FI/ct = (15.2)(0.325)/(2 - 1.34) = 7.5 in-k Section F.8.1.2 addresses elements in flexure (the web), for which Fb /W = 19.7 ksi. The allowable moment for tension in the web is M2 = FI/ct = (19.7)(0.325)/(2 - 1.34 - 0.125) = 12.0 in-k b) Section F.8.2 addresses compression. Section B.5.5.2 addresses elements in flexure (the web) with the tension edge supported and the compression edge free. The web slenderness is b/t = (2 - 0.125)/0.125 = 15, which is between S1 = 10.2 and S2 = 23 so Fb /W = 27.9 - 0.81(b/t) = 15.7 ksi The allowable moment based on web compression is M3 = (15.7)(0.325)/1.34 = 3.81 in-k The least of the allowable moments is M3 = 3.81 in-k, so 3.81 in-k is the allowable moment. Part II, channel with stiffener lips: The section properties are computed using the method shown in example 16 with the following results: c = 1.20 in. to the top fiber I = 0.461 in4
VII-45
a) Section F.8.1 addresses tension. Section F.8.1.1 addresses elements in uniform tension (the flange), for which Fb /W = 15.2 ksi, The allowable moment for tension in the flange is M1 = FI/ct = (15.2)(0.461)/(2 - 1.20) = 8.8 in-k Section F.8.1.2 addresses elements in flexure (the web), for which Fb /W = 19.7 ksi. The allowable moment for tension in the web is M2 = FI/ct = (19.7)(0.461)/(2 - 1.20 - 0.125) = 13.5 in-k b) Section F.8.2 addresses compression. Section B.5.4.1 addresses elements in uniform compression supported on one edge (the lip). The lip slenderness is b/t = (0.50 - 0.125)/0.125 = 3, so Fb/W = 15.2 ksi The allowable moment based on lip compression is M3 = (15.2)(0.461)/1.20 = 5.8 in-k
VII-46
Section B.5.5.1 addresses elements in flexure (the web) supported on both edges. The web slenderness is b/t = (2 - 2(0.125))/0.125 = 14 cc = -1.20 co = 2 -1.20 = 0.8 co /cc = 0.8/(-1.2) = -0.67 m = 1.15 + co /(2cc) = 1.15 + 0.5(-0.67) = 0.82 Since b/t = 14 < S1 = 54.9, Fb /W = 19.7 ksi The allowable moment based on web compression is M4 = (19.7)(0.461)/(1.20 - 0.125) = 8.4 in-k. The least of the allowable moments is M3 = 5.8 in-k, so 5.8 in-k is the allowable moment. NOTES: The use of Section B.5.5.1 assumes that the lip provides lateral support at the top of the web. Section F.8.2.3 may be used to determine the local buckling strength more precisely and check this assumption.
January 2010
Example 24 ALLOWABLE WEB STRESS IN A WELDED BEAM Illustrating Section B.5.5.1 SOLUTION: Assume that the neutral axis is approximately at the midheight of the web. For the web, b/t = 72/0.190 = 379 Section B.5.5 states that for elements in flexure, the stress corresponding to the flexural compression strength is Fb = Fbo(1 - Awzc /Agc) + Fbw Awzc /Agc where
Figure 24 GIVEN: 1. Beam cross section as shown in Figure 24 2. Alloy of web: 6061-T6 3. Structure type: building
Fbo = stress corresponding to the flexural compression strength calculated using Section B.5.5.1 for an element if no part of the cross section were weldaffected. Using Part VI Table 2-18 for unwelded allowable stresses, since b/t = 379 > 77 = S2: Fbo/W = 1563/(b/t) = 1563/379 = 4.1 ksi Fbw = stress corresponding to the flexural compression strength calculated using Section B.5.5.1 for an element if the entire cross section were weldaffected. Since the web is less than 0.375″ thick, regardless of the filler used, use Part VI Table 2-19W for the welded allowable stresses. Since b/t = 379 > 123 = S2: Fbw/W = 982/(b/t) = 982/379 = 2.6 ksi Awzc = cross sectional area of the weld-affected zone in compression Awzc = (1 in.)(0.190 in.) = 0.19 in2 Agc = gross cross sectional area of the element in compression. Agc = (72 in.)(0.190 in.)/2 = 6.84 in2 Fb = Fbo(1 - Awzc/Agc) + Fbw Awzc/Agc Fb /W = (4.1)(1 - 0.19 /6.84) + (2.6)(0.19) /6.84 = 4.1 ksi NOTES: Lateral-torsional buckling must also be checked using Section F.2. Filler metal for welds should be selected from Specification Table M.9.1.
REQUIRED: Allowable compressive bending stress at the extreme fiber of web.
January 2010
VII-47
Example 25 ALLOWABLE WEB STRESS IN A WELDED BEAM WITH STIFFENED WEB Illustrating Section B.5.5.3 where Fbo = stress corresponding to the flexural compression strength calculated using Section B.5.5.3 for an element if no part of the cross section were weldaffected. Using Part VI Table 2-18 for unwelded allowable stresses, since b/t = 379 > 173 = S2: Fbo /W = 3502/(b/t) = 3502/379 = 9.2 ksi Fbw = stress corresponding to the flexural compression strength calculated using Section B.5.5.3 for an element if the entire cross section were weldaffected. Since the web is less than 0.375″ thick, regardless of the filler used, use Part VI Table 2-19W for the welded allowable stresses. Since b/t = 379 > 275 = S2: Fbw/W = 2201/(b/t) = 2201/379 = 5.8 ksi Awzc = cross sectional area of the weld-affected zone in compression Awzc = (1 in.)(0.190 in.) = 0.19 in2 Agc = gross cross sectional area of the element in compression. Agc = (72 in.)(0.190 in.)/2 = 6.84 in2 Fb = Fbo(1 - Awzc/Agc) + Fbw Awzc/Agc Fb/W = (9.2)(1 - 0.19 /6.84) + (5.8)(0.19) /6.84 = 9.1 ksi Section B.5.5.3 provides requirements for the longitudinal stiffener as = 3.5, b = 72 in., t = 0.190 in., f = 9.1 ksi, s = 10 ft = 120 in. AL = 5.25 × 2.50 - 5.06 × 2.12 + 0.19 × 1.00 = 2.59 in2
Figure 25 GIVEN: 1. Beam cross section as shown in Figure 25. 2. Neutral axis of beam is at mid-height of web. 3. Vertical stiffener spacing 10 ft o.c. 4. Alloy of web: 6061-T6. 5. Structure type: building
[(
)(
]
6A 2 0.02αsftb3 IL= _________ 1 + ____ L __s + 0.4 E bt b
)
[(
)( )
]
2 ( )( ( ) ____ )( )( 72 )3 = _____________________ 0.02 3.5 9.1 0.19 1+ ________ 6 2.59 120 + 0.4 ( ) 10,100 72 0.19 72
IL = 28.3 in4 = the required moment of inertia of the longitudinal stiffner.
REQUIRED:
Actual moment of inertia = 1⁄3 (5.253 × 2.50 - 5.063 × 2.12 + 0.193 × 1.00) = 29.0 in4
1. Allowable web stress at the toe of the compression flange. 2. Confirm adequacy of the longitudinal stiffener.
The stiffener is therefore satisfactory.
SOLUTION: For the web, b/t = 72/0.190 = 379 Section B.5.5 states that for elements in flexure, the stress corresponding to the flexural compression strength is Fb = Fbo(1 - Awzc /Agc) + Fbw Awzc /Agc VII-48
The required distance from the toe of the compression flange to the centroid of the stiffener is 0.4(72)/2 = 14.4 in. NOTES: The notes of example 24 also apply to this example.
January 2010
Example 26 I-BEAM WITH WEB SHEAR CONTROLLING Illustrating Sections F.8 and G.2
Figure 26 GIVEN: 1. 8 in. × 5 in. Aluminum Association standard I-beam weighing 6.18 lb/ft (I 8 × 6.18) 2. Span: 4 ft, simply supported at ends. 3. Compression flange continuously laterally supported. 4. Alloy: 6061-T6. 5. Structure type: building
REQUIRED: Allowable uniform load.
SOLUTION: From Part V, Table 8, Aluminum Association standard I-beams. d = 8.00 in., b = 5.00 in., A = 5.26 in2, tf = 0.35 in., tw = 0.23 in., Ix = 59.7 in4, Sx = 14.9 in3 For the flange, b/t = (5.00 - 0.23)/2/0.35 = 6.8 For the web, b/t = (8.00 - 2(0.35))/0.23 = 31.7 Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below. Section F.1 establishes safety factors of 1.95 on tensile rupture and 1.65 on all other limit states for flexure of building-type structures. Because the compression flange is laterally supported, the beam is not subject to lateralJanuary 2010
torsional buckling. For open shapes not subject to lateraltorsional buckling, Section F.2 requires that Section F.8 be used to determine the flexural strength. Section F.8 addresses elements of flexural members. a) Section F.8.1 addresses tension. Section F.8.1.1 addresses elements in uniform tension (the flange), for which Fb/W = 19.5 ksi, Section F.8.1.2 addresses elements in flexure (the web), for which Fb/W = 27.6 ksi. b) Section F.8.2 addresses compression. Section B.5.4.1 addresses the flange; b/t = 6.8 > 6.7 = S1, so Fb/W = 27.3 - 0.91(6.8) = 21.1 ksi Section B.5.5.1 addresses the web; b/t = 31.7 < 49.3 = S1, so Fb/W = 27.6 ksi The least of these allowable stresses is 19.5 ksi; tension controls bending. Using an allowable stress of = 19.5 ksi Allowable moment = M = FS = 19.5 × 14.9 = 291 in-k Section G.1 establishes a safety factor of 1.65 for shear of building-type structures. Section G.2 addresses shear in flat webs supported on both edges. VII-49
For b/t = 31.7 < S1 = 35.3, Fs/W = 12.7 ksi, allowable web shear stress. Allowable shear = (Fs/W)Aw = (12.7 k/in2)(8)(0.23 in2) = 23.4 k From Part VI, Beam Formulas Case 6, for a simply supported beam with a uniform load,
Since w1, the allowable load for bending, is greater than w2, the allowable load for shear, the allowable load is w2 = 11.7 k/ft. NOTES: Section F.8.3, the weighted average flexural strength, could be used to determine a more precise and less conservative bending strength. Since shear controlled, however, using Section F.8.3 would not result in a greater allowable distributed load on the beam.
M = wL2/8, which can be written as w1 = 8M/L2, when w is unknown V = wL/2, shear at end of beam. Rearranging, w2 = 2V/L w1 = 8M/L2 = 8(291/12)/42 = 12.1 k/ft for bending. w2 = 2V/L = 2(23.4)/4 = 11.7 k/ft for shear
VII-50
January 2010
Example 27 WELDED CONNECTION Illustrating Section J.2
Figure 27 GIVEN: 1. Welded connection as shown in Figure 27 2. Longitudinal weld length 6 in. (each side), transverse weld length 4 in. 3. Weld size: Sw = 3⁄8 in. equal leg fillet 4. Base metal: 6061-T6 5. Filler alloy: 4043 6. Structure type: building
REQUIRED: Determine the allowable force P on the connection.
SOLUTION: Section J.2 establishes the allowable strength of welded connections as Rn/W, where W = 1.95 for building-type structures. Section J.2.2.1a) defines the effective throat of a fillet weld; the effective throat for an equal leg fillet is
Section J.2.2.2 establishes the nominal strength of a fillet weld Rn as Rn = FswLwe where Fsw is the lesser of: a) The product of the weld filler’s shear ultimate strength and the effective throat. The 4043 filler’s shear ultimate strength is taken from Table J.2.1 as 11.5 ksi. Fsw = (11.5 k/in2)(0.265 in.) = 3.0 k/in. b) The product of the base metal’s welded shear ultimate strength and the fillet size Sw. The 6061-T6 base metal welded shear ultimate strength is taken from Table A.3.5 as 15 ksi.
e = 0.707Sw
Fsw = (15 k/in2)(0.375 in.) = 5.6 k/in.
e = 0.707(0.375 in.) = 0.265 in.
The lesser of these is 3.0 k/in., so
Section J.2.2.1b) defines the effective length Lwe:
P = Rn/Ω = Fsw Lwe /Ω = (3.0 k/in.)(16 in.)/1.95 = 24.6 k
Lwe = 2(6 in.) + 4 in. = 16 in. > 4Sw = 4(0.375 in.) = 1.5 in., so the full length of the weld is effective. The length of the end-loaded fillet weld is 6 in. < 100 (0.375 in.) = 37.5 in., which does not exceed the maximum effective length prescribed in Section J.2.2.1. January 2010
NOTES: The strength of aluminum fillet welds is usually governed by the strength of the filler alloy, as in this example. Therefore, the joint strength can be increased by using a stronger filler, such as 5356. Table M.9.1 shows which fillers may be used. VII-51
Example 28 OPEN SHAPE IN BENDING Illustrating Sections F.1.1.1, F.2.1, F.2.2.1, F.2.2.3, and F.8.1.1 GIVEN:
At any point x between supports 1 and 2,
1. Twin span curtainwall I-beam as shown in Figure 28d 2. Beam cross section and properties as given in Figure 28e 3. Uniform wind load of 26.3 lb/ft2. Load must be applied as both a pressure (positive inward) and suction (negative) loading. Beams are spaced 5 ft o.c. 4. Lateral bracing provided at anchors and at horizontals 5. Alloy: 6063-T5 6. Structure type: building
REQUIRED:
2 M(x) = R1x - ___ wx 2 2 3 wLx - ___ = __ wx 8 2
()
2 L ___ Mmax= w 8
M1= ____ 9 w L2 128
Check the given I-beam’s ability to carry the wind load safely.
Since the loadings and support conditions are identical in spans 1 and 2, only span 1 will be reviewed.
SOLUTION:
Since the load acts both inward and outward, four possible failure modes exist. These include failure due to:
From Part VI, Beam Formulas Case 36, continuous beam of two equal spans-uniformly distributed load: Load, w = (26.3 lb/ft2) (5 ft) (1 ft/12 in.) = 11.0 lb/in. (positive and negative)
For the interior flange: 1. extreme fiber tensile stress 2. extreme fiber compressive stress For the exterior flange: 3. extreme fiber tensile stress 4. extreme fiber compressive stress 1. First consider pressure (inward) loadings:
Figure 28b
(A) Consider extreme fiber tensile stresses: Conservatively use the lesser of allowable tensile bending stresses for the web and flange elements. From Part VI, Table 2-20, Section F.8.1.1
Figure 28a
Fb = 9.7 ksi For the beam, the maximum moment occurs at support 2: wL2 = (11.0)(150) M = ___ __________2 = 30,940 in.-lb max 8 8
VII-52
January 2010
This results in the maximum extreme fiber tensile stress, which occurs in the exterior flange:
L 24 __b = ____ = 48
Mc (30.94)(6.00 - 3.05) f = ___ = ________________ = 8.1 ksi < Fb; b I 11.28
From Section F.2.1,
ry 0.50
Fb /Ω = 10.5 - 0.036(48) = 8.8 ksi
therefore, it is satisfactory.
) ( )( fb= ___ Mc = ___________ 30.94 3.05 = 8.4 ksi < Fb/Ω; I 11.28
(B) Consider extreme fiber compressive stresses: Allowable compressive stresses are a function of the unbraced length (Lb) and the compression flange geometry. Compressive stresses must therefore be reviewed at the various combinations of moment and unbraced length. Span 0′ to 2′
Lb (in.) 24
Mmax (in.-lb) 11,680
Compression flange Exterior
2′ to 10′-6″
102
17,400
Exterior
10′-6″ to 12′-6″
24
30,940
Interior
therefore it is satisfactory.
2. Next, consider suction (outward) loadings:
(1) From 0′ to 2′: To determine the slenderness ratio
L ______ b___ , the bending coefficient Cb may be conservatively r y √ Cb taken as 1:
L 24 __ b = ____ = 28.6 ry 0.84
From Section F.2.1,
Figure 28c (A) Extreme fiber tensile stresses are similar to those under pressure loading, therefore, it is satisfactory by inspection (B) Consider extreme fiber compressive stresses:
Fb /Ω = 10.5 - 0.036(28.6) = 9.5 ksi (________________ )( 6.00 - 3.05 ) fb= ___ Mc = 11.68 = 3.05 ksi < Fb/Ω; I 11.28
therefore it is satisfactory.
(2) From 2′ to 10′-6″: To determine the slenderness L ratio ______ b___ , the bending coefficient Cb may be conservary √ Cb tively taken as 1: L 102 __ b = ____ = 121.4 ry
0.84
From Section F.2.1, 87,000 Fb/Ω = _______ = 5.9 ksi ( 121.4 )2 ( )( 3.05 ) fb= ___ Mc = ________________ 17.4 6.00 - = 4.6 ksi < Fb/Ω;
I
11.28
therefore it is satisfactory.
(3) From 10′-6″ to 12′-6″: To determine the slenderness L ratio ______ b___ , the bending coefficient Cb may be conservary √ Cb tively taken as 1: January 2010
Span 0′ to 2′
Lb (in.) 24
Mmax (in.-lb) 11,680
Compression flange Interior
2′ to 10′-6″
102
17,400
Interior
10′-6″ to 12′-6″
24
30,940
Exterior
(1) From 0′ to 2′: To determine the slenderness ratio
L ______ b___ , the bending coefficient Cb may be conservatively r y √ Cb taken as 1:
L 24 __ b = ____ = 48 ry 0.50
From Section F.2.1, Fb /Ω = 8.8 ksi ) ( )( fb= ___ Mc = ___________ 11.68 3.05 = 3.2 ksi < Fb/Ω; I 11.28
therefore, it is satisfactory.
(2) From 2′ to 10′-6″:
L To calculate the slenderness ratio ______ b___ , the bending ry √ Cb coefficient Cb must be calculated. To calculate Cb, determine the moments at the quarter-point, midpoint, and three-quarter VII-53
point of the span from 2′ to 10′-6″, in accordance with Section F.1.1.1:
location quarter-point
x 49.5
moment (in.-lb) 17,100
midpoint
75
15,400
= MB
three-quarter point
100.5
6,600
= MC
2 _____ 3wLx - ___ wx
8
2
= MA
[
( )]
√
A = 1.92 in2 (area of full section) This section is singly symmetric, so Section F.1.1.2 may be applied to determine Cb. The moment of inertia of the compression flange about the y-axis is Icy: Icy= ___ 1 ( 0.125 )( 1 )3 + ___ 2 ( 0.625 )( 0.375 )3 12 12 2 1.75 + 2( 0.375 )( 0.625 ) ____ - _____ 0.375 2 2
2 Mmax= _____ 9wL = 17,400 in-lb 128
(
12.5Mmax Cb= ________________________ 2.5Mmax+ 3MA+ 4MB+ 3MC (
I 11.28 Sc= __ x = _____ = 3.70 in3 cx 3.05 __________ Fet Me= AFey U + U2+ r 2o ___ Fey
)
Icy = 0.237 in4
)
12.5 17400 = _____________________________________ 2.5( 17400 )+ 3( 17100 )+ 4( 15400 )+ 3( 6600 )
I 0.237 cy __ = _____ = 0.26 < 0.9, and 0.26 > 0.1, so Iy 0.92
Cb = 1.23 L ______ ____ b___ = _________ 102 = 183.9 ry √ Cb 0.50√1.23
π2E π2(10,100) F = _____ __________ = = 4.56 ksi ey 2 ky L_ (1.0)(102) 2 b ___ ________ ry 0.69
From Section F.2.1,
U = C1go + C2 j
87,000 Fb/Ω = _______ = 2.6 ksi ( 183.9 )2
From the commentary for Section F.1.1.2, for continuous beams loaded as shown in the top two cases of Figure CF.1.1, C1 = 0.41Cb and C2 = 0.47Cb.
( ) (
) ( )( fb= ___ Mc = __________ 17.4 3.05 = 4.7 ksi > Fb/Ω; I 11.28 therefore it is not satisfactory.
So C1 = 0.41 (1.23) = 0.50 and C2 = 0.47(1.23) = 0.58
Redetermine the allowable stress using the effective ry from Section F.2.2.1. This allows use of equation F.2-2:
( )( ) ]
√
L 2 I yd J rye= ___ 1 ___ ±0.5 + 1.25 + 0.152 __ __b Iy d 1.7 Sc calculated by taking Iy, Sc, and J as though both flanges were the same as the compression flange with the overall depth remaining the same. Because the load is on a flange and acts in a direction away from the shear center, the plus sign in front of “0.5” is to be used (see note 2 below also). ______________________________________ ________________________
√ 3.65 [
go = distance from the shear center to the point of application of load go = 6 - c = 6 - 4.31 = 1.69 in. (+ since load acts away from the shear center)
____________________________ _________________
√ [
)
)]
( )( ( ) )
Iy 2 cy j = 0.45d _2I ___ - 1 1 - __ f I Ix
Eq. F.2-8
for singly symmetric sections. smaller flange area = Afi = (1) (0.125) + 2(0.625)(0.375) = 0.594 in2
) ( 0.48 ) 6 ( 102 0.033 _____ rye= ___ 1 _______ + 0.5 + 1.25 + 0.152 _____
larger flange area = Afe = (2)(0.125) + 2(0.375)(0.50) = 0.625 in2
rye = 0.837 in.
Afi /Afe = 0.594/0.625 = 0.95 > 0.8, so j may be taken as - yo = - (y coordinate of the shear center)
Alternately, use the provisions of Section F.2.2.3 to determine rye:
yo = - (4.31 - 3.05) = - 1.26 in.
1.7
√
( 0.48 )(
2
6
Compare this with the more accurately calculated j:
____
L Me rye= ____ b ___
√
1.2p ESc
Lb = 102″, E = 10,100 ksi VII-54
(Eq. F.2-3)
df = distance between flange centroids df = 6 - 0.260 - 0.375/2 = 5.55 in. January 2010
From Section F.2.1, Fb/W = 9.5 ksi
Note: 0.260 is the calculated distance from the extreme fiber of the interior flange to the centroid of the interior flange.
( ( ))
0.92 j = (0.45)(5.55)[2(0.26) - 1] 1 - _____ 11.28
2
Mc _____ 30.94(2.95) f = ___ _____ = 8.1 ksi < F /Ω; = b b I 11.28 therefore, it is satisfactory.
= -1.20 in.
The given I-beam is therefore satisfactory to carry the required wind load.
Note the two values for j are approximately equal. U = C1go + C2 j = (0.50)(1.69) + (0.58)(-1.20)
ro = (r x2 + r y2 + xo2 + yo2 )1/2
NOTES: 1. The equation used for rye was chosen because the load is applied at the exterior flange. In cases where the load is applied at one of the flanges, the following table can be used to determine the correct sign:
rx = 2.42, ry = 0.69, xo = 0, yo = 4.31 - 3.05 = 1.26
Beam/load combination
ro = (2.422 + 0.692 + 02 + 1.262)1/2 = 2.81 in.
(a) Load promotes buckling
U = 0.149 in.
(
)
Sign –
1 π2EC ___ ___w Fet = ___ GJ + Ar o2 L 2t
Compression
Tension
Tension
Compression
Lt = 102 in., G = 3800 ksi
(b) Load resists buckling
+
Compression
Tension
Tension
Compression
(
)
1 π2(10,100)(6.11) Fet = __________ 2 (3800)(0.0293) + _____________ (1.92)(2.81) (102)2 Fet = 11.2 ksi
If the load is applied to the web (i.e., near the neutral axis), use the first equation given in Section F.2.2.1.
Now evaluating the equation for Me:
[
√
( )]
Fet M = AF U + U2 + r 2 ___ e ey o Fey
[
√
( )]
M = (1.92)(4.56) 0.149 + 0.1492 + 2.812 11.2 ____ e 4.56 Me = 39.9 k-in. ____
____________
2. Since the moment is greater between supports than at the ends, Cb can be taken conservatively as 1.0. 3. The beam must also be checked for local buckling. For the flange, Section B.5.4.3, flat elements with one edge supported and one edge with stiffener, applies if Ds/b < 0.8; however,
L Me ____ 39.9 rye = ____ b ___ = 102 ____________
Ds/b = (0.625 - 0.125)/[(1.75 - 2(0.375) - 0.125)/2] = 0.5/0.4375 = 1.14 > 0.8,
rye = 0.884 in.
so Section B.5.4.3 cannot be applied. Using instead Section B.5.4.1, flat elements supported on one edge,
√
√
1.2π ESc 1.2π (10,100)(3.70)
Lb _________ 102 _ _____ __ = ____ = 104 rye√Cb 0.884√1. 23 From Section F.2.1, Fb /Ω = [10.5 - 0.036(104)] = 6.8 ksi > fb; therefore it is satisfactory.
b/t = (1.75 - 0.125)/2/0.125 = 6.5 < 8.2 = S1, so Fb/W = 9.7 ksi Checking the web (Section B.5.5.1, flat element with both edges supported): b/t = (6 - 0.125 - 0.125 - 0.125)/0.125 = 45 < 62.9 = S1
(3) From 10′-6″ to 12′-6″: conservatively take Cb =1
So Fb/W = 12.6 ksi
Lb /ry = 24/0.84 = 28.6
So local buckling does not govern any of the above checks.
January 2010
VII-55
4. In order to minimize the calculations shown, some cases not governing were noted to be satisfactory by inspection or were not done. In general, both flanges need to be checked at all critical moment locations (particularly for unsymmetrical sections).
Figure 28d VII-56
January 2010
Figure 28e
January 2010
VII-57
Example 29 FORMED SHEET IN BENDING Illustrating Sections B.5.4.2, B.5.5.1, F.8.3, J.8.1, L.3 and 1.4
Figure 29 GIVEN: 1. 8 in. rib panel, repeating pattern. 2. Thickness = 0.032 in. 3. Alclad 3004-H151 (Fcy = 28 ksi, Ftu = 34 ksi, Fty = 30 ksi) (Table A.3.4). 4. Bend radii are 0.0625 in. at inner surface of each bend. 5. Structure type: building
REQUIRED: 1. Allowable bending moments for: a. top in compression b. bottom in compression 2. Moment of inertia for deflection calculations 3. Allowable reactions: a. interior b. exterior 4. Check the applicability of calculations for the above against the criteria of Section 1.4.
SOLUTION: 1. Allowable bending moments for: a. top in compression b. bottom in compression VII-58
This siding is the 8″ ribbed siding shown in Part V Table 25 with section properties given in Part V Table 26. Calculations of Section Properties The small radii are ignored. Nodal geometry is based on points of intersection of centerlines of elements. Nodal geometry Node 1 2 3 4 5
x 0.000 1.375 1.875 7.500 8.000
y 0.016 0.016 0.984 0.984 0.016
Element Properties Element 1 2 3 4 Totals
y 0.016 0.500 0.984 0.500
L 1.375 1.090 5.625 1.090 9.179
yL 0.022 0.545 5.535 0.545 6.647
y2L 0.000 0.272 5.446 0.272 5.992
I 0.000 0.085 0.000 0.085 0.170
January 2010
ct = SyL/SL = 6.647/9.179 = 0.724 in., height of neutral axis Ix = [S(y2L) - c2t SL + SI]t = [5.992 - (0.724)2(9.179) + 0.170](0.032) = (1.349 in3)(0.032 in.) Ix = 0.0432 in4 Sbot = Ix /ct = (0.0432)/(0.724) = 0.0596 in3 Stop = Ix /(height - ct) = (0.0432)/(1 - 0.724) = 0.1565 in3
Allowable Moments Weighted average allowable moments are determined from Section F.8.3. For the top in compression and the bottom in tension: The allowable moment for compression is Mactc = (2.8)(0.0342)/(0.984 - 0.724) + (22.1)(0.0089)/(1 - 0.032 - 0.724) = 1.17 in-k
The moment of inertia of the flanges (elements 1 and 3) is
If = [(1.375)(0.724 - 0.016)2 + (5.625)(0.984 - 0.724)2] (0.032) = 0.0342 in4
The allowable moment for tension is
The moment of inertia of the webs (elements 2 and 4) is
Mattc = (17.4)(0.0342)/(0.724) + (23.6)(0.0089)/ (0.724 - 0.032)
Iw = [2(1.090)(0.724 - 0.5)2 + 2(0.085)](0.032) = 0.0089 in4
Allowable compressive stresses Allowable compressive stresses are determined for each element using the appropriate section of the Specification. For example, for element 3, Section B.5.4.2 applies (flat element in uniform compression). b/t = 5.625/0.032 = 175.8
= 1.13 in-k; since 1.17 > 1.13, compression governs and Matc = 1.13 in-k
For the bottom in compression and the top in tension: The allowable moment for compression is Macbc = (11.3)(0.0342)/(0.724 - 0.016) + (22.1)(0.0089)/(0.724 - 0.032) = 0.83 in-k
Since b/t > S2 = 41,
k2 √BpE _________________ 2.04√(39.3)(10,100) F/W = ________ = (1.6b/t)W 1.6(175.8)(1.65)
The allowable moment for tension is
Matbc = (17.4)(0.0342)/(1 - 0.724) + (23.6)(0.0089)/(1 - 0.032 - 0.724)
= 2.8 ksi
The table below summarizes results for all elements.
Element 1 2 3 4
Length 1.375 1.090 5.625 1.090
Spec. B.5.4.2 B.5.5.1 B.5.4.2 B.5.5.1
b/t 43.0 34.0 175.8 34.0
Allowable Compressive Stress (ksi) 11.3 22.1 2.8 22.1
Allowable tension stresses For elements in uniform tension, the allowable tensile stress
= lesser of (Fty/1.65, Ftu/1.95) = lesser of (30/1.65, 34/1.95) = lesser of (18.2, 17.4) = 17.4 ksi
For elements in flexural tension, the allowable tensile stress
= lesser of (1.3Fty/1.65, 1.42Ftu/1.95) = lesser of ((1.3)(30)/1.65, 1.42)(34)/1.95) = lesser of (23.6, 24.8) = 23.6 ksi
January 2010
= 3.0 in-k; since 0.83 < 3.0, compression governs and Mabc = 0.83 in-k
The above results can be converted to allowable moments per foot of width as follows: Matc = (1.13)(12 in./ft.)/(8 in./cycle)
= 1.69 k-in./ft-width (top in compression)
Mabc = (0.83)(12 in./ft.)/(8 in./cycle)
= 1.24 k-in./ft-width (bottom in compression)
2. Moment of inertia for deflection calculations Refer to Section L.3 π2E π2(10,100) For element 1: Fe = _______ 2 = _________2 = 21.1 ksi (1.6b/t) (1.6(43)) > 11.3 ksi = fa so the width of element 1 is not reduced for deflection calculations.
VII-59
π2E π2(10,100) For element 3: Fe = _______ = ___________ = 1.3 ksi (1.6b/t)2 (1.6(175.8))2 < 2.8 ksi = fa
The allowable interior reaction, Fint is Fint = (Pc/Ω)(2 webs/cycle)(12 in./ft.)(1 cycle/8 in.) (1000lb/k) = 563 lb/ft-width.
so the effective width of element 3 is be = b (Fe /fa)½ = 5.625 (1.3/2.8)½ = 3.77 in.
Section J.8.3, combined web crippling and bending, should also be considered.
Similarly, it can be seen that elements 2 and 4 are not reduced. A recalculation of the moment of inertia follows:
b. Allowable end reaction Let the bearing length, N, be 2.0 in. Again, consider element 2. 1.2C wa(N + Cw2) P c /Ω = _____________ ΩC wb
Element Properties Element 1 2 3 4 Totals
y 0.016 0.500 0.984 0.500
L 1.375 1.090 5.625 1.090
Leff 1.375 1.090 3.77 1.090 7.325
yLeff 0.022 0.545 3.71 0.545 4.822
y Leff 0.000 0.272 3.65 0.272 4.19 2
Ieff 0.000 0.085 0.000 0.085 0.170
ct = S(yLeff)/SL = 4.822/7.325 = 0.658 in., height of neutral axis Ix = [S(yL 2eff) - ct2 SLeff + SIeff]t = (4.19 - (0.658)2(7.325) + 0.170)(0.032) = (1.189 in3)(0.032 in.) = 0.038 in4, for deflection calculations when element 3 is at its allowable compressive stress.
1.2(0.0215)(2.0 + 1.3) P c /Ω = __________________ = 0.100 k per web. (1.95)(0.435) The allowable end reaction, Pend, is: Pend = (Pc/Ω)(2 webs/cycle)(12 in./ft.)(1 cycle/8 in.) (1000 lb/k) = 301 lb/ft-width 4. Check the applicability of calculations for the above against the criteria of Section 1.4. Cases (a), (b), and (e) do not apply. Cases (c), (f), and (g) vary with each installation.
3. Allowable reactions: a. allowable interior reaction Reference: Section J.8.1 Let the bearing length, N, be 2.0 in. Consider element 2 (a web). ( N + C w1 ) C P c /Ω = ___________ wa ΩC wb
where C wa = 0.0215 k [see (a) above] Cw2 = 1.3 in. Cwb = 0.435 in. [see (a) above]
Case (d) is checked as follows:
____
where Cwa = t2 sin q (0.46 Fcy + 0.02 √EF cy ) where t = 0.032 in. q = 63.4° Fcy = 28 ksi E = 10,100 ksi so Cwa = (0.032)2 ___________ sin63.4° (0.46(28) + 0.02 √(10,100)(28) ) Cwa = 0.0215 k Cw1 = 5.4 in. Cwb = Cw3 + Ri (1 - cos q) where Cw3 = 0.4 in. Ri = 0.0625 in. so Cwb = 0.4 + 0.0625 (1 - cos 63.4°) Cwb = 0.435 in. (0.0215)(2.0 + 5.4) so P c/Ω = ________________ = 0.188 k per web (1.95)(0.435)
maximum b = 5.625 + 2(0.25) = 6.125 in. b/t = 6.125/0.032 = 191 Condition (1) is stated then algebraically rearranged. (1) b/t < _____ 1230 otherwise tests are required. 3 __ √ q
q < (1230/(b/t))3 q < 265 psf
Condition (2) is treated likewise _____
(2) b/t < 435 √ F ty /q otherwise tests are required.
q < [435/(b/t)]2Fty q < [435/191]2(30) q < 155 psf
Subcase (2) governs. Tests must be run to establish the load carrying capacity of the panel when: a. q > 155 psf b. Cases (c), (f), or (g) are not satisfied.
VII-60
January 2010
Example 30 SCREW CONNECTION Illustrating Section J.5 c) Section J.5.6.3 addresses screw shear. The single shear strength of a ¼″ 7075-T73 machine screw is given in Part VI, Table 5-1 as 1170 lb. Rn /(1.25Ω) = (1170 lb)/(1.25(3)) = 0.31 k The allowable shear is the least of 0.24, 0.31, 0.32, and 0.31 k, so the allowable shear is 0.24 k based on bearing on the top sheet. 2. Allowable tensile force
Figure 30
The allowable connection tension is determined according to Section J.5.5, which specifies a safety factor W = 3.0 for screw connection tension for building-type structures.
1. Tapping screw of 7075-T73 aluminum, ¼″ diameter, UNC thread joining 0.06 in. thick 3003-H16 sheet on top of 0.06 in. thick 5052-H32 sheet. 2. 5⁄8″ outside diameter flat washer under the screw head. 3. The hole diameter in the top sheet is 9⁄32″. 4. Distance from center of screw to edge of sheet is 1 in. 5. Structure type: building
Section J.5.5 requires that the washer outside diameter Dw equal or exceed 5⁄16 in.:
GIVEN:
REQUIRED: The allowable shear and tension forces for the connection.
Dw = 5⁄8 in. > 5⁄16 in. a) Section J.5.5.1 addresses pull-out. The allowable pull-out force is Rn /Ω = KsDLeFty2/Ω = (1.01)(0.25)(0.06)(23)/3 = 0.12 k b) Section J.5.5.2 addresses pull-over. The allowable pull-over force is:
SOLUTION: 1. Allowable shear force The allowable connection shear is determined according to Section J.5.6, which specifies a safety factor W = 3.0 for screw connection shear for building-type structures. a) Section J.5.6.1 addresses bearing. Since the edge distance is 1 in. > 0.5 in. = 2(¼ in.) = 2D, the allowable bearing force is 2FtuDt/W. Using Ftu from Table A.3.4, the allowable shear for bearing is Sheet
Alloy
Thickness (in.)
Ftu (ksi)
1 2
3003-H16 5052-H32
0.06 0.06
24 31
2FtuDt/W (k) 0.24 0.31
Rn /Ω = Cpovt1Ftu1(Dws - Dh)/ Ω = (1.0)(0.06)(24)(0.625 - 9/32)/3 = 0.16 k c) Section J.5.5.3 addresses screw tension. The tensile strength of a ¼″ diameter 7075-T73 machine screw is given in Part VI, Table 5-1 as 1940 lb. Rn /(1.25Ω) = (1940 lb)/(1.25(3)) = 0.52 k The allowable tension is the least of 0.12, 0.16, and 0.52 k, so the allowable tension is 0.12 k based on pull-out.
b) Section J.5.6.2 addresses screw tilting. Since t2 = 0.06 ≤ 0.06 = t1, the allowable screw tilting shear is Rn/W = 4.2(t 23D)1/2Ftu2/W = 4.2(0.063 × 0.25)1/2(31)/3 = 0.32 k
January 2010
VII-61
Example 31 WEIGHTED AVERAGE BENDING STRENGTH Illustrating Section F.8.3 GIVEN: 1. Symmetric Shape: Aluminum Association standard I 12 × 14.3 d
12″
bf
7″
tf
0.62″
tw
0.31″ 52.9 in3
Sx web height h flange area web area
10.76″ = 12″ - 2(0.62″) 7(0.62) = 4.34 in2 10.76(0.31) = 3.34 in2
Unsymmetric Shape: Modified I 12 × 14.3 (top flange 1″ wide instead of 7″ wide) d
12″
bf (bottom)
7″
bf (top)
1″
tf
0.62″
tw
0.31″
web height h
10.76″ = 12″ - 2(0.62″) 7(0.62) = 4.34 in2 1(0.62) = 0.62 in2 10.76(0.31) = 3.34 in2
bottom flange area top flange area web area
2. Alloy: 6061-T6 3. Continuous minor axis lateral bracing 4. Structure type: building
REQUIRED: The allowable bending moment about the major axis for each shape for loading causing compression in the top flange
SOLUTION: Allowable stresses for 6061-T6 given in Part VI Table 2-19 are used below. Symmetric Shape: Aluminum Association standard I12 × 14.3: Compression Section B.5.4.1: Flange: b/t = (7″ - 0.31″)/2/(0.62″) = 5.4 < 6.7 = S1, so Fc/W = 21.2 ksi Section B.5.5.1: Web: b/t = (10.76″)/(0.31″) = 34.7 < 49.3 = S1, so Fb/W = 27.6 ksi Tension Section F.8.1.1: Flange: Ft/W = 19.5 ksi Section F.8.1.2: Web: Fb/W = 27.6 ksi VII-62
Figure 31 If = 2[(7″)(0.62″)3/12 + (7″)(0.62″)(6″ - 0.62″/2)2] = 281.3 in4 ccf = 12″/2 - (0.62″/2) = 5.69″ ctf = 12″/2 = 6″ Iw = (0.31″)(10.76″)3/12 = 32.2 in4 ccw = ctw = 10.76″/2 = 5.38″ From Section F.8.3, the allowable bending moments are: (Fb/W)Iw (21.2)(281.3) (27.6)(32.2) c/W)If Mac = (F ______ + _______ = ___________ + __________ ccf ccw 5.69 5.38 = 1213 in-k (Fb/W)Iw (19.5)(281.3) (27.6)(32.2) t /W)If Mat = (F ______ + _______ = ___________ + __________ ctf ctw 6 5.38 = 1079 in-k The allowable bending moment is the lesser of Mac and Mat, which is Mat = 1079 in-k. January 2010
Unsymmetric Shape: Modified I 12 × 14.3 (top flange 1″ wide): Determine moment of inertia: A
y
Ay
d
Ad2
I 0.14
Ad2 + I
bottom 4.34 11.69 flange
50.73 3.14
42.79
web
3.34 6
20.04 2.55
21.72 32.18 53.9
top flange
0.62
total
8.3
0.31
0.19 8.24
42.10
0.02
42.93
Tension Section F.8.1.1: Flange: Ft /W = 19.5 ksi Section F.8.1.2: Web: Fb /W = 27.6 ksi If = 42.93 + 42.12 = 85.05 in4 ccf = 8.55″ - 0.62″/2 = 8.24″ ctf = 12″ - 8.55″ = 3.45″ Iw = 53.9 in4 ccw = 7.93″ ctw = 2.83″
42.12
From Section F.8.3, the allowable bending moments are: 70.96
106.61 32.34 139
The neutral axis is located (70.96 in )/(8.3 in ) = 8.55″ below the top of the section. 3
2
Compression Section B.5.4.1: Flange: b/t = (1″ - 0.31″)/2/(0.62″) = 0.6 < 6.7 = S1, so Fc /W = 21.2 ksi Section B.5.5.1: Web: b/t = (10.76″)/(0.31″) = 34.7 The neutral axis is located 8.55″ - 0.62″ = 7.93″ below top end of web and 10.76″ - 7.93″ = 2.83″ above bottom of web.
(F (21.2)(85.05) c /W)If b /W)Iw M = (F ______ _______ ___________ + (26.9)(53.9) __________ ac ccf + ccw = 8.24 7.93 = 402 in-k (F (19.5)(85.05) t /W)If b /W)Iw = (F ______ _______ ___________ + (27.6)(53.9) __________ M at ctf + ctw = 3.45 2.83 = 1006 in-k The allowable bending moment is the lesser of Mac and Mat, which is Mac = 402 in-k.
co/cc = 2.83/(-7.93) = -0.36, so m = 1.15 + (-0.36)/2 = 0.97. S1 = (Bbr - 1.3Fcy)/(mDbr) = (66.8 - 1.3(35))/[(0.97)(0.665)] = 33 < 34.7 = b/t, so Fb /W = Bbr/W - mDbr(b/t)/W = 66.8/1.65 - 0.97(0.665)(34.7)/1.65 = 26.9 ksi
January 2010
VII-63
Aluminum Design Manual
Appendix 1 SI Guide
Appendix 1 SI Guide
Table A.1 SI CONVERSION FACTORS Quantity Length
Area
Volume
Mass
Multiply
By
inch
in.
millimeter
mm
foot
ft
0.3048
meter
m
mile
mi
1.609
kilometer
km
millimeter
mm
0.03937
inch
in.
meter
m
3.281
foot
ft
kilometer
km
0.621
mile
mi
square inch
in2
square millimeter
mm2
January 2010
645.16
square foot
ft
2
0.093
square meter
m2
square mile
mi2
2.590
square kilometer
km2
square millimeter
mm2
0.001550
square inch
in2
square meter
m2
10.764
square foot
ft2
square kilometer
km2
0.386
square mile
mi2
cubic inch
in3
cubic millimeter
mm3
cubic foot
ft
0.028317
cubic meter
m3
cubic yard
yd3
0.765
cubic meter
m3
gallon (U.S. liquid)
gal
3.785
liter
L
quart (U.S. liquid)
qt
0.946
liter
L
cubic millimeter
mm3
61.024×10-6
cubic inch
in3
cubic meter
m3
35.315
cubic foot
ft3
cubic meter
m3
1.308
cubic yard
yd3
liter
L
0.2642
gallon (U.S. liquid)
gal
liter
L
1.057
quart (U.S. liquid)
qt
ounce
oz
gram
g
pound
lbm
kilogram
kg
kilogram
kg
3
short ton (2,000 lb)
Force
25.400
To obtain
16387
28.350 0.4536 907.2
gram
g
0.035274
ounce
oz
kilogram
kg
2.205
pound
lbm
kilogram
kg
0.001102
short ton (2,000 lb)
pound-force
lbf
4.448
newton
N
kip
k
4.448
kilonewton
kN
newton
N
0.2248
pound-force
lbf
kilonewton
kN
0.2248
kip
k
Appendix I-3
Table A.1 SI CONVERSION FACTORS (Continued) Quantity Bending Moment
Stress, Pressure
Energy, Work, Heat
Density
Angle
Temperature
Multiply
By
To obtain
pound-force-inch
lbf-in.
0.113
newton-m
N-m
pound-force-ft
lbf-ft
1.356
newton-m
N-m
newton-m
N-m
8.851
pound-force-inch
lbf-in.
newton-m
N-m
0.738
pound-force-ft
lbf-ft
pound-force per square inch
lbf/in2
6.895
kilopascal
kPa
pound-force per square foot
lbf/ft2
0.04788
kilopascal
kPa
inch of water
in. w.c.
0.249
kilopascal
kPa
kip per square inch
k/in
6.895
megapascal
MPa
kilopascal
kPa
0.145
pound-force per square inch
lbf/in2
kilopascal
kPa
20.885
pound-force per square foot
lbf/ft2
kilopascal
kPa
4.015
inch of water
in. w.c.
megapascal
MPa
0.145
kip per square inch
k/in2
foot-pound-force
ft-lbf
1.356
joule
J
British thermal unit
Btu
joule
J
calorie
cal
4.187
joule
J
kilowatt-hour
kW-h
3.600×10
joule
J
joule
J
0.738
foot-pound-force
ft-lbf
joule
J
0.948×10
British thermal unit
Btu
joule
J
0.239
calorie
cal
joule
J
0.278×10
kilowatt-hour
kW-h
pound per cubic foot
lb/ft3
kilogram per cubic meter
kg/m3
kilogram per cubic meter
kg/m
0.06243
pound per cubic foot
lb/ft3
degree
deg
0.017453
radian
rad
radian
rad
degree
deg
2
1055 6
-3
-6
16.0185 3
57.296
°C = (°F - 32)/1.8 °F = 1.8°C + 32
See ASTM E 380 for more information.
Appendix I-4
January 2010
Table A.2 SI PREFIXES Multiplication Factor
Prefix
Table A.3 SI DERIVED UNITS WITH SPECIAL NAMES Symbol
Quantity
Unit
Symbol
Formula
10
exa
E
force
1015
peta
P
pressure, stress
pascal
Pa
N/m2
1012
tera
T
energy, work
joule
J
N-m
109
giga
G
power
watt
W
J/s
106
mega
M
103
kilo
k
102
hectoa
h
101
dekaa
da
10-1
decia
d
10-2
centia
c
10-3
milli
m
10-6
micro
µ
10-9
nano
n
10-12
pico
p
10-15
femto
f
10-18
atto
a
18
newton
N
kg-m/s2
a: not recommended
January 2010
Appendix I-5
Aluminum Design Manual
Index
AASHTO, I-19 abrasion blasting, I-67 ACM, III-10 adhesive joints, III-11 aerospace, III-6, III-9, III-13 allowable strength design: I-16, I-30, II-9 tables by alloy-temper, VI-10-57 alloys: commonly used, III-6 comparative characteristics and applications, IV-17 designation system, cast alloys, IV-10 designation system, wrought alloys, IV-8 foreign designation systems, IV-21 metallurgy, IV-12 aluminum composite material, III-10 analysis, I-16, I-39, II-19 angles: equal leg, V-18, V-20 in flexure, I-45 in tension, II-21 section property formulae, V-44 square end, V-20, V-24 unequal leg, V-21 annealing, IV-7, 13, 15 anodizing, I-67, III-11, 17, 24, 40 ASCE, I-19 ASME, I-19 ASTM, I-19 automotive, III-3, 6, 8, 13, 24, IV-18 AWS, I-19 beams: angles, I-45 bars, I-45 examples, VII-8, 10, 12, 13, 28, 30, 36, 37, 39, 41, 43, 45, 47, 48, 49, 52, 58, 62 formulas, VI-82 round or oval tubes, I-45, 47, VII-12, 36 tubular shapes, I-45 welded, I-49 bearing: examples, VII-15, 16 on holes, I-57, 59, 62, VII-15 on flat surfaces, I-63 on slots, I-57 pins, I-63, VII-16 bending, I-67 coefficient, I-43, VII-54 developed lengths, VI-61 maximum thickness for 180 degree bends, VI-60 minimum radii for sheet and plate, VI-58 minimum radii for wire and rod, VI-60 biaxial stresses, III-9 block shear rupture, I-63 bolts: dimensions, VI-71 material, I-56
January 2010
shear, I-57 slip critical connections, I-58 spacing, I-57 tension, I-57 installation, I-58, 68 braces, I-84 bridges, I-16, 30, II-12, III-8 buckling: constants, I-31 , II-13, VI-5-8 local buckling effect on beam strength, I-45 local buckling effect on column strength, I-42 elastic buckling stresses of elements, I-38 lateral-torsional, I-43, 45, 46 torsional, I- 41 torsional-flexural, I-41 building codes, I-16, 30 building-type structures, I-16, 30 camber, I-16, 66, II-39 Canadian shapes, V-11, 16 castings: material specifications, I-21 mechanical property limits for permanent mold casting alloys, IV-23 mechanical property limits for sand casting alloys, IV-22 weld fillers for, I-70 channels, V-7-11 Aluminum Association Standard Channels, V-7, VI-63 American Standard Channels, V-8 Canadian Channels, V-11 Car and Ship Building Channels, V-10 clad alloys, IV-7 cleaning aluminum, I-67 coefficient: tension, I-21, II-9 thermal expansion, I-20, 67, 80, II-39 columns: I-16 examples, VII-18-27 member buckling, I-41 welded, I-42 combined stresses: compression and bending, I-52 shear, compression, and bending, I-52 tension and bending, I-52 web crippling and bending, I-64 compression: axial, I-41 concrete in contact with aluminum, I-68, II-41 conductivity electrical, IV-33-36, IV-5 thermal, IV-33-36, IV-5 connections: adhesive, III-11 mechanical, I-56 welded, I-54 contact with other materials, I-67, II-41
Index-3
corrosion, III-23 cathodic protection, III-24 crevice, III-23 galvanic, III-23 stress-corrosion cracking, II-40 corrugations, see building sheathing countersunk, I-57, 59, 62 cutting, I-67 damping, II-39 dead load, I-71, 79, II-13 deflection, I-66, 71, 72, III-6 density, I-20, IV-37 designation system for sections, V-5 diaphragms, III-9 doubly symmetric sections, I-43 drilling, see holes ductility, III-9 edge distance, see fasteners effective length factor, I-41 effective radius of gyration, I-43 effective width, I-66 elements: I-16 compression, I-33 edge stiffeners, I-34 flexure, I-36 intermediate stiffeners, I-36 curved, I-36 post-buckling strength, I-32 welded, I-33, 36 width defined, I-32 elevated temperatures, see heating emittance, III-26 erection, I-68 examples, VII-1-63 existing structures, I-83 extrusions, III-14 alloy selection, III-17 circle size, III-18 design, III-16 finish, III-16 joining, III-21 screw slots, III-22 shapes, III-14 fabrication, I-67-68, III-7 layout, I-67 tolerances, I-38 factor of safety, see safety factors fasteners: I-21 fatigue: I-73, II-46, III-7 allowable stress range, I-73 constant amplitude fatigue limit, I-73, 78 constant amplitude loading, I-73 design details, I-74 examples, VII-30, 34 stress category, I-77 variable amplitude loading, I-73
Index-4
finishes: I-67, II-40, IV-6 fire: I-79 fire protection: III-25 forgings, I-19 gages, sheet metal and wire, V-40 grip, I-16, 59 heating, I-20, 67, 79, II-40, IV-5 holes: bolts, I-57, 58 drilling, I-67 punching, I-67 reaming, I-67 rivets, I-59 screws, I-60, 62 I-beams: Aluminum Association Standard I-beams, V-12, VI-64 American Standard I-beams, V-15 inquiries, I-4 interpretations, I-4 joining, see connections laps, see roofing and siding connections light poles, see luminaires live load, I-71, 79, II-13 load and resistance factor design, I-17, 30, II-9 load combinations, I-17, 30, 66, 79 load factors, I-17, II-13 lockbolts, I-58 luminaires, I-19, 30, 77 magnesium content in aluminum alloys, I-20, 21, III-23, IV-12 marine service, I-20, 21, IV-12 material specifications, I-21 mechanical properties: fastener alloys, IV-24 for wrought aluminum products, I-22 for welded aluminum products, I-26 permanent mold alloys, I-28, IV-23 sand casting alloys, I-28, IV-22 testing to determine, I-71 typical, IV-25 modulus of elasticity, I-12, 22-27, IV-25 net area, I-40, II-20 nomenclature, see symbols nuts, I-21, VI-73 paint, I-67, 68, II-40, III-6, IV-6 physical properties, typical, IV-33 pipe, I-47, III-8, V-32 pipe bursting pressure, III-9 plate, I-19, 21 Poisson’s ratio, I-20 polar radius of gyration, I-15, V-4, 11, 12, 14, 16, 17 postbuckling, I-17, 32, II-18 pressure vessels, III-8, IV-18, 19 punching, see holes radiographic inspection, I-21, II-10 radius of gyration, I-15, V-4
January 2010
rail cars, III-8, IV-17 reaming, see holes recycling, III-26 references, I-19, II-50, III-7, 27 reflectance, III-26 Research Council on Structural Connections, I-20, 58, 68 resistance factors, I-30, II-12 rivets: bearing, I-59 blind, I-59 heads, I-68 hole, I-59, 68 hollow-end, I-59 material, I-59 removal, I-68 shear, I-59 spacing, I-59 steel, I-59 roofing and siding: allowable deflection, I-72 connections, I-64 dimensions, V-38 example, VII-58 maximum recommended spans, VI-66-68 section properties, V-39 testing, I-72 weights, V-38 safety factors: I-30, II-12 sandwich panels, III-10 section properties, I-30, II-12, V-1 serviceability, I-66 screw chase, I-17 screw slot, I-17, 61, III-22 screws, tapping: example, VII-61 hole sizes, I-60 internal thread stripping area, VI-73 material, I-59 pull-out, I-60 pull-over, I-62 shear, I-62 tension, I-60 screws: cap screws, strengths, VI-70 machine screws, tensile and shear strengths, VI-69 sheet metal screws, shear strengths, VI-70 sections, nomenclature, V-5 shear, see webs in tubes, I-51 shear center, I-15 shear modulus, I-12, 20 sheet, I-19 sheet gages, V-40 ships, III-18 SI conversions, Appendix I siding, see roofing and siding
January 2010
singly symmetric sections, I-43-44 slenderness ratio, I-15 specific gravity, IV-5, 37 specific heat, I-80 stability, I-39, II-19 stainless steel, I-19, 57, 59, 67 steel, I-67, III-6 bolts, see bolts, steel fatigue performance, III-7 rivets, see rivets, steel stiffeners: circumferential stiffeners on tubes, I-52 edge, I-34 example, VII-34, 43, 45, 48 intermediate stiffeners, I-36 longitudinal, I-37 transverse stiffener in web, I-50 strengths, see mechanical properties sustainability, III-26 symbols, I-11 tanks, III-8, IV-17, 18 tapered thickness elements, I-33, II-15 tees, V-25-26 Army-Navy, V-26 Special, V-26 temperature, effect on strength, I-20, IV-38 tempers, IV-13 tension, axial: I-40 example, VII-6, 7 tension, beams, I-47 testing, I-71 mechanical properties, I-71 structural performance, I-71 torsion: and bending, I-52 in tubes, I-52 torsional flexural buckling, I-41 torsion constant, I-13, II-12 tread plate, I-20, VI-65 triaxial stresses, III-9 tubes: circumferentially welded, I-36, 42, 49 column examples, VII-24, 26, 27 in bending, I-47 rectangular, V-36 round, V-28 shear, I-51 square, V-34 unbraced length, I-13, 18 unsymmetric sections, I-44 V-beam, see building sheathing vibration, I-66 von Mises stresses, III-9 warping constant, I-11, V-4, 7, 11, 12, 14, 16, 17, 41 washers, I-58, 60, 62
Index-5
webs: crippling, I-64 crippling example, VII-11, 60 examples of shear checks, VII-47, 48, 49 longitudinal stiffeners for, I-37, VII-48 shear in stiffened webs, I-50 shear in unstiffened webs, I-50 transverse stiffeners for, I-50, VII-34 weighted average strengths axial compression, I-42 bending, I-48, VII-62 weights, V-6 welding: beams, see beams, welded columns, see columns, welded
Index-6
corners, II-42 fabrication, I-68, II-41 filler wire, I-21, 69, 70 fillet welds, I-55, VI-76-77, 80-81 groove welds, I-54, VI-74-75,78-79 inspection, I-68 lap joints, II-42 plug and slot welds, I-55 post-weld heat treating, I-56, II-33 stud welds, I-56 wide flange sections, V-13, 14, 17 wind load, II-39, VII-12, 52 wood, I-67, II-41 zees, V-27
January 2010
